You can buy a simcard at most stores/airports for a pound and then top it up over the phone. I personally use giffgaff because for £10/month you can get unlimited internet data, unlimited texts, and like 250 mins. Best deal I found so far!
Also, you can order a free sim from any company you choose to go with. If you want to have a contract phone, you'll probably have to pay a deposit first to get it.