A mortgage dictates who's responsible for paying off a loan on a house. It does not determine who the legal owner of the house is. It's possible for the wife to be an owner of the house if her name is on the deed and not the mortgage, so that's something the poster may want to make arrangements for.
The Guardian first reported in May that the house in Clacton, which Farage initially said he had bought himself, is in fact wholly owned by Laure Ferrari, his long-term partner. While Farage said the arrangement was because of security reasons, Ferrari purchasing the house would have saved the Reform UK leader an estimated 44,000 in the higher rate of stamp duty to which he would have been liable, given he already owns other properties.