The simple answer is 'yes' .... all British spiders bite; otherwise they wouldn't be able to eat. However, most of them would not bite a human because they would not regard us as food. Those that do bite us don't have the strength to bite through human skin, so worry ye not about a British spider taking a great lump out of you.
If you want to be fussy, the answer is "No". Spiders don't bite. They stab their victims injecting venom which contain enzymes that break down tissue. They then suck the broth out of the body and discard the body-shell. (hope you have finished your lunch comloulou). There are no native spiders in the UK that are dangerous to humans.