Shops like O2, Carphone Warehouse,EE, etc are only asking for your address to send you Spam mails, etc.
Instead, as already mentioned by a few posters, you can often buy SIM Card for ANY network for only £1 from supermarkets, ethnic mobile shops, etc. without ANY Questions asked.
Quite often, if you also buy top-ups at the same time, they will throw the SIM card for free.