I know this question is about Xmas Day, and I might be stating the obvious, but I think literally any day other than the 25th shouldn't be a problem. Xmas eve, Boxing day, NYE - if you ring up agencies (in London at least) they all have girls available on those days. Girls available on AW too. I imagine other UK cities are the same.
The thing about a punt on Christmas Day is, if you're going to have to pay a premium, is it really worth it? I presume a majority of girls would want more money because in all honesty, it's likely to be inconvenient for them. Of course, if you find a girl who's open for business at normal prices, then why not. But if that's as difficult to find as I suspect it could be, I reckon just crack on with whatever else on Xmas Day (pub?), and treat yourself to a bird in the run up to New Year.