LocalBitcoins is hands down our favourite option. Handling millions of dollars worth of transactions each day, it's the main meeting place for everyone looking to either buy or sell Bitcoin.
If you find it difficult to use, keep scrolling.
Bittylicious is a peer to peer platform that allows buying, selling and trading Bitcoin with ease. Payments can be made via cash at UK corner stores, instant UK bank transfers, credit cards, SEPA bank transfers or mobile banking platforms such as Paym and Pingit.
Coinbase is a trustworthy service that sells Bitcoin and accepts most credit & debit cards. They do require photos of your ID for Know Your Customer (KYC) and Anti Money Laundering (AML) reasons, but they are one of the most versatile services out there.
Another good UK option is Indacoin (much pricier, but they don't require registration and don't do tedious KYC & AML checks).