Visiting the UK for 3 Months

[Meow Meow]

So here's the situation. My boyfriend lives in the UK and I would like to visit him for 3 months. I've never been there before. We are both really worried about when I get up to border control whether or not they'll let me through.
I have proof that I'll be returning home when the 3 months are up. I have a work confirmation letter that states permission for my 3 month leave. I have a return ticket. And I have a dog that I would like to return to and don't want to be away from for more than 3 months.

Our concern is will it be a problem staying with him as his girlfriend? When they ask me where I'm staying or who I'm staying with or what our relationship is with each other, is there a chance I will be turned away?

Also one other question:
What is the ideal amount of funds to have for a three months stay, given that I don't have to pay for hotels or anything of that matter. I've already calculated everything out. The only things I have to really worry about is food and occasionally going out. Plane tickets are already paid for. Just an idea from other's experiences would be nice.