This happened to mine I thought it was dead, and I just chopped it down and dug the roots up, took ages! Then about two weeks later I was listening to gardeners question time on radio four and there was a question about it, and as far as I remember they just said to cut the top off down to where the new growth is and it should be fine and just carry on growing, the tops dead though. Hope this helps

As you live in the UK, I can only think you actually mean you have a Cordyline, not a date palm (Phoenix dactilyfera) which isn't hardy in Britain. If it is a Cordyline australis, this behaviour is typical - it probably got damaged at the growing tips during the unusually severe winter, so if its growing at the base and not anywhere else, saw it down to where the new growth is, preferably at an angle to allow rain to run off. The new growth will take over.