If your phone isn't unlocked, you can't use another SIM card in it when you're in the UK. I recently used my iPhone in the US, and it was VERY expensive to use abroad. If you need to text your boyfriend and grandmother when you land, it shouldn't be more than $1-$2 per text. However, I wouldn't recommend using it for any more than that. Turn off data roaming and only use the iPhone for wireless. If you need to make calls, use Skype on wireless. I even keep my phone on airplane mode at all times when I'm abroad, just to make sure I don't get any charges, then turn it off when I want to use the wireless.
When I first moved to the UK, I had a cheap PAYG T-Mobile phone. I think the phone was £30-£50, and I put £20 credit on it. If you're going to be in the UK a lot, you could always get a cheap PAYG phone. If it's just one trip, though, it may not be worth it.