Arbitrator can determine the proper law
The significance of the international arbitration is that one of the foreign legal system and a foreign country is involved, thus they have the ease to affect the deal with the procedural rules and the legal issues of the dispute, it also has a bearing on the cost, the obtaining of the evidence and enforcing an award in a country which may be different from that of the dispute.  The question that needs to be in mind while resolving a dispute is that what will be the principles for establishing, which applicable laws will be applied to the arbitration. 
S (46) (3) of the Arbitration Act 1996  , “is concerned with the situation in which there is no express choice of law, and here the arbitrators are empowered to determine the conflict of laws rules which should apply, and then to apply those conflict of laws rules to decide which law should apply to the contract."  The question that arises is that the choice suggested by the arbitrator of the applicable rules is that correct and secondly is its application a correct. It is however stated that if the arbitrator has to decide under the English court jurisdiction then the English law would be applicable under the Rome Convention 1980  and is therefore stated that if it is not decided with certainty then the that law is decided to which the contract is most closely connected to. 
In an submission to an agreement it is important to choose the relevant laws that will be applicable in an agreement because if they are expressly stated then in that way they are substantive issues to the disputes and its always better to draft them in a submission agreement, but if the express and the implied choice of law is not made by the parties then in that case the choice of law is determined by the law of seat of the arbitration and the contract as a whole as well. 
The Seat of arbitration is described in the S (3) of the Arbitration Act 1996  which describe that it is essential to have seat for arbitration which defines the geographical location of the arbitration as well as the procedural law, the seat may be different as well e.g. The LCIA ( London Court Of International Arbitration Rules). 
A number of cases in different jurisdiction which has taken the law appropriate to govern the arbitration agreement. The case of C V D  this case emphasis on the even though, in the contract it was stated that, the contract is to be governed by the New York law, the Court of Appeal decided that English law will apply, because it was expressly stated by the parties that any in case of any dispute the issue will be finally resolved in London under the Arbitration Act 1996. To support the judgment the English court gave a list of cases to support the idea, where it was stated that the case will be decided according to the English law where it was made specific that Arbitration Act 1996, other cases such as, Xl insurance Ltd v Owens corning  and Noble assurance company and shell petroleum inc v Gerling Konzern general Insurance Company Uk branch  . In the case of Black Clawson  it was stated that it would be a rare case in which the law of arbitration would not be a seat of arbitration.
The case of James Miler v. Whitworth Street Estates  here the House of Lords ruled that the Arbitration will be governed by the place of proceeding, notwithstanding the English law governed the law of contract 
Bulbank case  where an issue arose as the arbitration agreement for void for breach of an allegedly implied terms, in which it was stated by the Swedish court that a “No particular provision concerning the applicable law for the arbitration agreement itself was indicated [by the parties], In such a circumstances the issue of the validity of the arbitration clause should be determined in accordance with the law of the state in which the arbitration proceedings have taken place, that is to say Swedish law"
James Miller & partners Ltd v. Whitworth Street Estate (Manchester Ltd)  it was an English company but the part appointed the Scottish arbitrator in order to resolve the dispute. The proper law would be English but the actions of the both the parties indicated that the Scottish law should be governed
REC wafer Norway AS (Formerly REC Scanwafer AS). Moser Baer Photo Voltaic Ltd  In this particular case the parties applied to both India and England, here the injunction was refused by the English court as the parties cannot apply to both countries for a relief.
Chalbury McCouat International Ltd v.PG Foils Ltd  in this case it was stated that where the applicable law will be English as stated by the parties intention then the laws of Europe or England shall be applied, depending on the seat of arbitration.
The cases such as Matermaco V PPM  and Chloc Z Fishing v Odyssey Re  , it was stated that FFA controls the interstate or foreign commerce transaction and in that case even the English court is mentioned but the New York convention and the FFA will be applied to the convention, once the federal arbitration act is applied then it rules will however be applied.
The French courts have adopted a different approach in the sense, that they says that the governing law will be determined by the parties’ common interest, and the arbitration agreement remain independent of various national law. In the case of Dalico  , “by virtue of a substantive rule of international arbitration, in this the issues was to be seen as to parties main intention. 
It is important that the parties should determine the procedural law and which law is to be applied but if they have not done that then, It is very important for an arbitrator to distinguish between the procedural and substantive law, The Lexfori and the procedural law, when a arbitrator has to choose the appropriate law it has two step process firstly is that which conflict of rules of the country has to apply and secondly according to those rules which law shall apply.  In determining the substantive law the Committee for International commercial arbitration of the ILA states in its recommendation that uniformity, and should determine the law from the parties as well as should not bring up legal issues which can cause disputes among the parties.  However there has been artificially has been seen in determining the substantive law, The Rome convention  Its article states that the choice of law should made ‘expressed or demonstrated with reasonable certainty’ 
In a report by professors Guiliano and Lagarde, which stated that “the parties may have made a real choice of law, although not expressly stated in their contract, but that the court is not permitted to infer a choice of law that the parties might have made"  If the parties have not made a express choice of law regarding their arbitration then lexfori , which is the law of forum as well is where if they have chosen a certain country then that country law shall apply.
In the absence of law the most important point is where you have to choose the seat of arbitration, if the parties have not chosen a seat, in that case generally the institution choose one for them. It is however stated that that “The London court of international Arbitration (LCIA) rules provide that a absent part agreement, the seat will be London, unless the court decides otherwise after hearing from the parties".  The world intellectual property organization, international chamber of commerce and the arbitration institute of the Stockholm chamber of commerce rules all provide for institutional determination.  The International Bar arbitration sets out supplementary rules of evidence which can supplement and fill in the gap in the arbitration of different countries, where the domestic rules are very comprehensive 
There should be a clear distinction between the Lex Arbitri and the substantive law of the contract, where the parties choose a place where there is no connection to the place. Mostly in the absence of law or the expressed choice of the parties, arbitrator do is they apply the UNCITRL rules which state “shall apply the law determined by the conflict of laws rules of law which it considers to be most appropriate"  .
The ICC rules also govern the place of the arbitration if the parties have not agreed to a certain decision and it does its best to choose a place which best favors the arbitration.
The seat theory however gives a an established legal framework to n international commercial arbitration, so instead of floating around the arbitration has a legal framework , rather than looking at other national laws, however the Lex arbitri ensures that the arbitral process works with certainty. In the case of Halpern v Halpern  it ensured that parties are free to choose the law and the procedure of the arbitration process. 
The UNIDROIT principles ‘they represent the system of contract law and they only apply if the parties have agreed to apply them in their contract will be governed by the general principal or the Lex Merctoria’. 
The Delocalization is a theory in which it states that international arbitration should be be related to the local law of the place where the arbitration occur the delocalization is a theory which is not concerned with the disputes between the parties who are not its citizen it is however stated that the delocalization should be detached from the law of seat i.e. situs  , but on the other hand it is argued that every arbitration is done according to the mandatory law and under a territory and to ensure a check of arbitration procedure and evidence or there is no defraud the state need to keep a check on them, one in 1984  it was that where the parties were not citizens of Belgium and they had no business here were not to apply in Belgium, however due to less arbitration issues in Belgium, they had to change their law in 1998.however nowadays the parties prefer the less delocalized arbitration reason being that it is they want court supervision. So now territory rule prevails over delocalization. 
Jan Paulson stated “Those who reject the delocalization process seem to mistake the purpose of permitting parties to unbind arbitrations from the law of situs of proceedings it is wrongly decided to sought as an escape from national jurisdiction"  It is however stated that the de facto rule of the ICC would thus become the place of the arbitration in the absence of contractual stipulation  cases which support the following statement are the Gotaverken case  , S.E.E.E v. Yugoslavia 
In awarding and arbitral award to the parties the arbitrator should be work with certainty and must not excess his powers in the case of “Anisminic and Harrow school, the Lord Diplock and John Donaldon emphasized that the judicial boldness should be exercised in with review to commercial arbitration and they should act in a proper way"  Mann stated “No one can ever or anywhere been able to point to any provision or legal principle which could permit individual to act outside the confines of a system of municipal law" 
In order to make a decision for the arbitration in absence of a express choice applicable rules should be applied and there is no universal rule for international arbitration, so follow the seat of arbitration, some national laws including the Dutch, French and Swiss, carry a logical conclusion by abandoning the reference to conflict rules altogether they allow an arbitral tribunal to decide for itself what rule of law the tribunal should consider appropriate to settle the dispute. The ICC and UNCITRL model law play an important role.  It is advisable for the parties to choose the applicable law in the contract because sunder S (29) of the Arbitration Act 1996 arbitrator has the immunity for any decision made in the arbitration unless he acted in bad faith, arbitration decision can be unfair for some parties’ as well regarding the applicable law applied.
C V D  EWHC 1541 (comm.)
Xl insurance Ltd v Owens corning (2000) 2 Loyld’s Rep 500
Noble assurance company and shell petroleum Inc v Gerling Konzern general Insurance Company Uk branch (2007) EWHC 25322
Black-clawson v papierwerke ( 1981) 2 Lloyd’s rep 446, at 483
James Miller v. Whitworth Street Estates (1970) 1 All E.R 796 ( H.L)
REC wafer Norway AS (Formerly REC Scanwafer AS). Moser Baer Photo Voltaic Ltd2010) EWHC, 2581
Chalbury McCouat International Ltd v.PG Foils Ltd2010) EWHC, 2050
Matermaco V PPM (2000) XXV ,YBK ,Comm Arb.
Chloe Z fishing Co Inc v Odyssey Re, 109 F supp 2d 1236 (SD cal 2000)
Gotaverken and Berardi v. Clair, (1981) 30 I.C.L.Q. 385-387
S.E.E.E v. Yugoslavia (1974) 5 pp.240-241