UK actually handed me a SIM at the Airport (or did I just pick it up from a counter) and I used it throughout my stay for a few months. Isn't that the case anymore?
It's generally the case that if you want a prepaid SIM card, you go to pretty much any shop to buy it for a nominal fee (usually just £1, but shops that rip you off may charge up to £5 in some cases). As soon as you buy and activate a top-up voucher, you are good to go. At no point is your identity or a card payment required.