AFAIK there is 2 major p2p trading sites... Localbitcoins and Bitbargain. Bitbargain is almost always overpriced though.
The other exchanges are very very strict in terms of buying BTC, AML and KYC in the UK so they require lots and lots of ID.
Good luck.
Yep... i had trouble trying to buy BTC in the UK with major exchanges, they're just way too strict in terms of depositing and withdrawing fiat currency. That's why I recommend you to use Localbitcoins.