Claimants loss and defendants gain
Restitution “at the claimant’s expense" requires that the claimant’s loss correspond exactly to the defendant’s gain
We all know that there is a significant distinction between restitution of an unjust enrichment and restitution for wrongs. Therefore, “at the claimant’s expense" is also used in different sense for the restitution of an unjust enrichment and restitution for wrongs. When “at the claimant’s expense" is used for the restitution of an unjust enrichment it means by subtraction from the claimant. For example, if A mistakenly pays to B £50 then defendant’s gain of £50 is by subtraction from the claimant of £50. However, if “at the claimant’s expense" is used for restitution for wrongs then it simply means by doing a wrong to the claimant. For example, if B pays £50 to A to beat C then C can only claim £50 from A by showing restitution for wrong of trespass to the person. As the law of restitution developed more and more in recent years we are faced with two important issues that arise in relation to the “at the expense of the claimant" in its subtractive sense. First question is of correspondence or equivalence between the claimant’s loss and the defendant’s gain. Second question is, “What happens when there is a third party involved?" i.e. Can claimant have restitution against defendant where benefit has been conferred by a third party? 
At the Expense of the Claimant:
For the claimant to succeed in a claim for restitution he must show that the defendant has acquired benefit at his expense. First, it provides the plaintiff right to pick up the person who has been enriched at his expense out of the masses. Second, anyone cannot sue the defendant for unjust enrichment. Law is very clear on this and says that only the person at whose expense the defendant is unjustly enriched can succeed against him in a claim for restitution.  The courts in Chase Manhattan NA v. Israel-British Bank (London) Ltd held that the claimant must show that there is a connection between the defendant’s gain and claimant’s loss in order to succeed in a claim for restitution.  For example, If A is unjustly enriched at the expense of B then C cannot sue A and claim A’s benefit. It is B and only B who can sue A and succeed in a claim for restitution.
Correspondence or Equivalence between Claimant’s Loss and Defendant’s Gain:
It is generally seen that in claims for restitution there is equivalence between the loss of the claimant and the gain of the defendant. For example, if A mistakenly pays £50 to B then B’s gain of £50 corresponds to A’s loss of £50. We can say that there is corresponding or equivalent plus and minus.
The courts in Re BHT (UK) Ltd held that there must be a correspondence between defendant’s gain and claimant’s loss. In that case: bank had a charge over the company’s book debts. The company went into liquidation and the receivers paid money to the bank on the assumption that the charge was a fixed charge. Later it was held by the Privy Council that the charge was a floating charge and not a fixed charge and so the money should not have been paid by the receivers to the bank. Following the decision of the Privy Council, the company brought a claim for restitution against the bank and sought to recover the money under unjust enrichment. The company’s claim against the bank failed. Following the principle of correspondence courts held that the bank was not enriched at the company’s expense. It stated that after company’s liquidation company was not entitled to the value of the book debts and thus did not suffer any loss.
However, this does not happen in every case. We know that in restitution for wrongs claimant can get more than his loss. This is one reason claimant will go for restitution for wrongs and not for normal remedy of compensation. But what happens in cases involving restitution for unjust enrichment? It has been established by the courts especially in cases where non-money benefits are involved that there need not be equivalence between the claimant’s loss and the defendant’s gain. For example, if defendant uses the claimant’s bicycle without permission for a day and returns it undamaged then the defendant’s enrichment may exceed any loss suffered by the claimant.  In BP Exploration Co (Libya) Ltd v. Hunt (No.2), Robert Goff J said that where the benefit does not consist of money, the defendant’s enrichment will rarely be equal to the plaintiff’s expense. 
The courts in Kleinwort Benson Ltd. v. Birmingham City Council held that correspondence between the defendant’s gain and claimant’s loss is not necessary for the claimant to succeed in a claim for restitution. In that case: under the interest rate swap agreement the plaintiff bank paid a net sum of £353,321.91 to the defendant council over the five years from September 1982. It subsequently became clear as a result of a decision in a separate case that the agreement is ultra vires the council and void. The bank brought an action for restitution of the money. The council sought to amend its defence and counterclaim to plead that it would be inequitable to order restitution because the sum the bank had paid out under the void agreement had been made good by the proceeds of hedging contracts in the money market. The judge refused leave to amend and gave final judgement in favour of the bank. 
On the other hand, it is not sufficient to say that defendant’s gain is at the expense of the claimant simply because there is ‘But for’ a causal link between defendant’s gain and the loss of the claimant. This is for the simple reason that it will extend the ambit of cases falling under unjust enrichment too far. The courts in Sempra Metals v. IRC held that the claimant could not have recovered the profits made by the defendant’s out of the mistakenly paid advanced corporation tax and the profits were casually linked to the subtraction from the claimant. Therefore, they were not gained “at expense of the claimant".
The Third Party Question:
Generally, for the claimant to succeed in a claim for restitution against the defendant he must show that the defendant is unjustly enriched at the claimant’s expense i.e. the defendant’s gain has come directly from the claimant. This is known as “the privity principle". For example, if the claimant has mistakenly paid £50 to the defendant then the defendant’s gain has directly come from the claimant i.e. defendant is unjustly enriched at the expense of the claimant. The same was held by the courts in Chase Manhattan NA v. Israel-British Bank (London) Ltd. The main rationale behind the privity principle is that the claimant who seeks to obtain restitution on the ground of unjust enrichment must show that he or she has a stronger claim to the value received by the defendant than the defendant’s claim to retain that value. 
However, there are certain “exceptions to the privity principle". They are-
Restitutionary claims to vindicate the claimant’s proprietary rights:
Where the defendant has received property in which the claimant has proprietary interest the claimant will be able to bring a restitutionary claim against the defendant even though the defendant received the benefit indirectly.
Restitutionary claims founded on wrongdoing:
Where the claimant’s claim for restitution is founded on a wrong it is irrelevant that the defendant obtained a benefit indirectly and just by showing that enrichment is caused by the wrong committed by the defendant against the claimant, without any need to show that the defendant’s benefit corresponds to the claimant’s loss, is sufficient.
Where a benefit is transferred from the claimant to the defendant by the claimant’s agent the claimant will be able to bring a restitutionary claim against the defendant even though the defendant is an indirect recipient of the enrichment. This is simply because the agent acts on behalf of his or her principal so the transfer is deemed to have been directly at the claimant’s expense.
Where a third-party intends to transfer a benefit to the claimant but mistakenly transfers the benefit to the defendant instead of claimant. The claimant can bring restitutionary claim against the defendant to recover the benefit. One reason to allow this is to avoid multiplicity of proceedings i.e. instead of third-party claiming it from the defendant and claimant claiming it from the third-party, claimant can claim it directly from the defendant and thus the third-party is discharged from its liability to pay to the claimant.
Theory of Interceptive Subtraction:
Prof. Peter Birks introduced the theory of “Interceptive Subtraction" to explain whether subtraction has occurred in situations where defendant has received enrichment from a third party. According to the theory of interceptive subtraction, if the wealth in question would have arrived in the plaintiff if it had not been intercepted by the defendant en route from the third party then it is true to say that the plaintiff has lost by the defendant’s gain. The theory of interceptive subtraction is based on the element of certainty that the plaintiff would have obtained the wealth. For example, plaintiff owed money from a third party but third party paid money to the defendant, then according to this theory existence of an obligation makes it certain that the plaintiff would have received the money had it not been intercepted by the defendant. 
In Official Custodian for Charities v. Mackey (No.2) it was stated by Nourse J that the case of a person who wrongly collects another’s rents is treated as an example of a wider class of case where the defendant, intervening without right between the plaintiff and a third party, renders himself accountable to the plaintiff for the sum which he received from the third party. It is of the essence of all those cases both that there is a contract or some other current obligation between the third party and the plaintiff on which the defendant intervenes and that the third party is indebted to the plaintiff in the precise amount of the sum which he pays to the defendant, so that he cannot claim repayment from the defendant in the face of a claim made against the defendant by the plaintiff. It is that which enables the plaintiff to sue the defendant without joining the third party, who no longer has any interest in the subject matter of the suit. It would be a waste of time and money if the plaintiff had to sue the third party and the latter had to sue the defendant. The suit for money had and received avoids circuity of action.