Speaking in very general terms, the law of England and Wales allows for the recovery of payments made by mistake. See, for example, Virgo, The Principles of the Law of Restitution (2015) at p 157:
A claim to recover money mistakenly paid by the claimaint to the defendant is often regarded as the paradigm example of a restitutionary claim founded on the unjust enrichment principle. In such a case there is clearly an enrichment at the claimant's expense and, at least where the reason for the claimant making the payment arose from a mistaken belief that he or she was liable to pay the money to the defendant, there is a clear justification for restoring the value of the money to the claimant, since the claimant's intention to make the payment can readily be treated as vitiated by the mistake.
Further information is freely available in the Wikipedia article on Barclays Bank Ltd v W J Simms, Son and Cooke (Southern) Ltd  1 QB 677. Although the basic principle is simple, the concept of "mistake" contains a lot of complexity, and there are various defences available to a claim in unjust enrichment, such as change of position. This is particularly relevant if the mistake is not brought promptly to the payee's attention.
Therefore, the question "can the person keep the repayment?" cannot be answered definitively. However, to a first approximation, the answer is "no."