Do you have a driving licence? If so try using that as proof of identity - not only do all modern style UK driving licences include a shot of the licence holder but they also have the person's name, address and date of birth on the card. If you do have a driving licence then try submitting that and you should be able to verify your age that way.
If you've got a driving licence but have still only got one of the old style licences then apply to the DVLA for a duplicate driving licence, saying that you've misplaced the first one. You'll have to pay a small charge to get a new one, and you'll have to supply a photo if you've never had a photographic UK driving licence before, but once that's done and you've got the replacement licence back again you should be able to use it to verify your identity, including being able to use it in order to prove to eBay that you are legally old enough to purchase the items that you are trying to buy.
