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Consummation of the marriage, according to Dr Lushington in D v A (1845) 163 ER 1039, requires "ordinary and complete" rather than "partial and imperfect" sexual intercourse, including erection and penetration but not necessarily leading to orgasm. It certainly need not result in conception, and the fact that the husband may be sterile or the woman barren is legally irrelevant.
Either party can seek an annulment on the grounds of incapacity. The incapacity may be physical or psychological, and may not prevent intercourse with anyone other than the spouse, but must be permanent and incurable. The fact that the parties may have had successful intercourse before the marriage is irrelevant if the incapacity existed at the time of the marriage; it is not clear how the law would view a case in which (say) the incapacity was the result of a road accident between the church and the honeymoon hotel.
Potter v Potter (1975) 5 Fam Law 161, CA
H and W married, and found W was physically unable to consummate the marriage. W underwent surgery and they tried again, but were prevented by W's emotional state. H then declined to try further and W petitioned for annulment on the grounds of H's wilful refusal. The judge dismissed the petition and W's appeal also failed: H's refusal was the result of his loss of sexual ardour rather than a deliberate decision.
Ford v Ford  Fam Law 232, Judge Goodman
H and W had a sexual relationship until H was sent to prison. They married while he was in prison, but he refused to consummate the marriage at the time and later said he did not want to live with W even after he was released. W's petition for a decree of nullity was allowed: H's refusal to consummate the marriage in prison was not a "wilful refusal", but his clear determination never to do so was sufficient.
Where the parties jointly regard some other act (usually a religious ceremony) as necessary before consummation, refusal to participate in this other act will be regarded as refusal to consummate.
A v J (Nullity)  1 FLR 110, Anthony Lincoln J
H and W were of Indian ancestry and took part in an arranged civil marriage, which was to be followed by a religious ceremony some four months later. Between the two ceremonies they spent only a few days together because of H's work in the USA. Shortly before the religious ceremony (which it was accepted was a prerequisite to consummation), W refused to go ahead with it, giving as her reason H's apparently uncaring and unloving attitude towards her. H apologised and said he had supposed a formal relationship would be appropriate until they were "properly married", but W refused to accept this apology and maintained her refusal to go through with the religious ceremony. H was granted a decree of nullity for W's wilful refusal to consummate the marriage.