Linux (in my view) is unquestionably safer than XP.
Almost certainly, you would be using a version of Firefox in Linux, which is well supported by banks in the UK. There is no reason your login should be rejected just because of the operating system you are using.
I use Linux all the time for on-line banking with no issues at all.
If you want the safest option of all, do your on-line banking from a live Linux CD, which of course, cannot be written to.