Buying a SIM card in The UK?

I'll be spending the upcoming semester studying abroad in London. I'm very attached to my phone and I have to bring it with me to stay connected back home. A friend of mine already arrived in London and said that I wouldn't be able to buy a SIM card for my phone at all because my American credit card doesn't have a PIN number (that's what he was told by the representative at the Virgin store).

I'm wondering how I can get a SIM card for my unlocked iPhone. I would be looking for either a "pay as you go" type SIM card or a month-to-month SIM card because I'll only be in the country for 6 months. Any speculation as to why my credit card may not be able to purchase the SIM?

-looking for a SIM only plan (carrier doesn't matter to me)
-have a chip-and-signature card that doesn't have a PIN number
-looking to buy it when I arrive in London from a store rather than online

You can use a credit card that doesn't have a chip in most shops in the UK. Worst case, SIM cards are cheap and you can buy one with cash. Then top up (phone credit) via the cellular provider's website (no chip needed) . I use Vodafone.