Musa Basjoo is pretty root hardy, and commonly they do resprout, unless the soil has suffered an unusually sharp frost by the standards of lowland Britain. I hope you mulched well around the base.
Keeping a banana pseudostem alive in your garden through the winter in Britain can be done, but it isn't easy, and depends on you being somewhere well sheltered from frost. Another option is to lift them and over-winter in a heated green house, which is what they do at a municipal garden near where I am writing from (Charing Cross, London). But that can be a big job.
But at least if they do regrow each year, and you feed and water them well, you should get an expanding clump of them, and that can be very attractive. Some people prefer it like that. If you keep the pseudostem alive for a few years, it will flower and die.