Yeah, as everyone said, definately have a return ticket otherwise, they probably won't let you in. Everytime I've flown to England, the first thing they ask to see is my return ticket.
The first time I ever flew to the UK, I was detained. I had met my boyfriend on-line, and when I mentioned that, they started hassling me with all these questions.
Do make sure you have more than enough money to support yourself if you do decide to stay for 6 months. If you don't, you run the risk of getting denied entry. That's another reason I was detained. I had only $475 on me for a 3 week stay. They interviewed my boyfriend, and luckily, he was able to show he could support me. I was told my immigration that I was VERY lucky that I was allowed to be able to get into the country cuz she said most people don't. There was another American girl that was being detained, and she was getting sent back.
I was detained for about 3 hours, and it was very scary! They kept interviewing me over and over again asking me the same questions and although I was telling the truth at all times, they said some of my answers sounded suspicious.
And yes, do take something to show that you have reason to go back to the US. Sometimes they ask you what you have to go back to...And avoid saying anything about a boyfriend unless you absolutely have to. Don't lie though cuz if you do and get caught, it's a big fine and you can be denied ever coming into the country again.
When I went in July, my immigration officer asked me if I had friends in the UK, and I said yes. I didn't go into detail, and he let me in. Basically, keep your answers concise unless asked to explain. I made the mistake of telling the immigration officer more than he needed to know the first time.
And just buy a return ticket for two weeks. Just because the ticket says you're returning in 2 weeks doesn't mean you can change your flight date.
If you have anymore questions about getting detained, I can answer them since it happened to me, and now I am traumatised when it comes to UK immigration cuz of how strict they are, haha.