The alarms and bells will happen on the
U.S. side if he transfers more than $10,000 into your account at any one time. He can send $9,900 with no problem but a $10K deposit will cause the bank to report you both to the IRS (and these days, probably to the terrorist watch list as well). At the UK immigration desk, as far as I have seen, they don't care how much money you bring over as long as it's enough to meet their requirements. Although, I suppose that if you looked very young and scruffy and were bringing $500,000 in your bank account, they might ask you where you got it.

When I came over for a one-year student visa, I brought about $15,000
in addition to the money for my course. I also had a letter from my mother stating that she would help me if I got in a jam, plus a copy of
her bank statement proving she could do so. I had a load of credit cards too, but he didn't ask about them.
They tend to get suspicious of anyone planning a visit of several months unless you can show them enough $$ in your bank account that you would not need to take a job in the UK, or apply for benefits, for the duration of your stay. You'll need three months of bank statements to satisfy them. The money doesn't have to be there for the entire 3 months; what they're looking for is proof that the account is in "normal use" rather than just a parking spot for money. They also sometimes ask people to show them the ATM card for the account, proving that you can access the money over here. You may get quizzed about large deposits but keep in mind that it is
not illegal for you to do what you are planning. If someone wants to give you money to visit the UK, and you honestly don't intend to overstay your visa, and you're not a criminal or planning criminal activities, then it's not a problem. The only problem is convincing them that you are not going to get married, and that you are going to leave, if they find out that you're coming to see a boyfriend. (Despite the way HM Immigration Service acts, it is still perfectly legal to come here on a visit and live with your boyfriend/girlfriend for six months.)
The cost of living is very high here and if it were me planning this trip, I'd aim for at least $5000. For a long visit, I would also have a list of specific things you are interested in doing while you are here. Just saying you are "traveling" may not cut it if you happen to get an IO who is having a bad day; be prepared.
One other thing...you probably know this, but it always bears repeating...
never, ever, lie to an immigration officer. Not only can it get you in a lot of immediate trouble if you are found out, but if you ever have to go to court with the Home Office about your immigration status, it can scuttle your case right away if they can prove you lied to them at any point during the process.
However, that being said, you do not have to
volunteer any information. It is their job to ask you questions and all you have to do is truthfully answer the questions that are asked--no more and no less. It's fine to say that you are coming to visit a "friend." But if they ask you "is this a boyfriend" then you have to tell them the truth.
Enough long-windedness from me....
Emily