Usually a recent letter from a government agency, showing your name and address, is adequate. Such as the DWP, Inland Revenue, NHS.
Have a look on the bank's website at what constitutes proof for them, if you need more ideas. Some banks may have a different list to others. I've heard the Post Office, Co-op and Halifax are relatively accommodating.
Another option sometimes available, is to have a parent or whomever you're staying with do a letter confirming you're resident there - you'll probably need to include proof of their ID and address too, though - or take that person along to the bank with you, to open the account.
Maybe approach a bank your relatives have a good relationship with.