I'm assuming that you're talking about coming to the UK on nothing but your passport... if I'm assuming incorrectly then ignore the rest of this post.
There are a lot of different threads in this room talking about this issue, and everyone seems to have a different opinion about it. Some people have done it without a hitch, over and over again. Some people haven't, and have either been turned away or detained and interrogated. You'rs truly falls into the latter category.
At the end of the day, your passport isn't a guarantee that they'll let you stay the 6 months allowed. If they don't believe your story, if they think you're trying to get around the system and get married in the UK without having gone the fiancee visa route, if they think you're going to stay illegally and try to get a job, if they think you don't have enough money to sustain yourself for the duration of your stay and thereby worry that you'll need to get a job illegally, or even if they are having a bad day and feel like being a jerk... they can turn you away. They don't have to give a good reason. The friendly arrangement between the US & the UK isn't a set-in-stone kind of thing... so no guarantees.
That being said, loads of people have done it without a hitch as I said.
My problem was that I was staying 5 months, didn't have enough money to live independently for that period of time, and it took them a LOT of convincing to believe that David was going to support me, that we weren't going to get married, that I was going back to the US after 5 months, and that I wouldn't get a job while I was here. A lot of convincing. Hours and hours and countless interviews of convincing.
You might have an easier time if you're only staying for 3 months as well, since that's less suspicious anyway.
So how about all of *THAT* for being vague and unhelpful!
Unfortunately this isn't a cut-and-dry issues, and everyone's circumstance is different. No two situations are the same, and so much depends on the person you get when you get to the Airport.
My Advice: have as much money as you can (Easier said than done, I know. We transfered loads of DAvid's money into my US account before I flew, and I just gave it back to him when I arrived. Wish we had transferred more money now!)... have your return flight tickets IN HAND so you can show them you have no intention of staying permanently, have a travel itinerary of things you want to do while you are here. They were annoyed that I said part of my reason for a 5 month trip was travel, but I didn't have any travel plans! It looked like I was lying.
So... that's my long-winded answer and I hope it's appropriate.
