As someone born and brought up in London who has visited the US almost 20 times I'd offer the following advice:
1) London Transport buses don't take cash payments - as others have mentioned, get Oyster cards as soon as you land and load them up with credit.
2) If you go into a pub for a drink (or something to eat) it's normal to order your drink (and more often than not your food) at the bar and then sit down.
3) The tap water is drinkable in London unless there is a notice by the tap (faucet to you, I guess).
4) We Brits despise people (fellow Brits and people from overseas) who jump the line (queue to us).
5) French fries are chips here and they come in a few varieties of thickness.
6) Chips are crisps here and the variety is mind boggling!
7) Theatres are where we go to see plays (stage shows). Cinemas are where we go to see movies.
8) Drinking alcohol outside on the street is not illegal and booze containers/bottles do not have to be concealed or wrapped up.
9) Drinking alcohol is not allowed on the London Underground system but is permitted on surface trains (British Rail or Network Rail as it's called locally).
10) Pizza pies are called pizzas. A pie to us is a pastry shell baked in a pie dish with a sweet or savoury filling and (usually) a pastry lid.
11) Money - 1p is a penny. £1 (one pound) is a quid. £5 is a fiver. £10 is a tenner. I don't think any other coins or notes have slang names for them. You may have trouble fitting British bank notes into a US wallet or purse as our notes are larger in size and get bigger the higher they are in value.
12) ATMs are also called cash machines or cash points.
13) If you're changing US Dollar cash or US Dollar traveler cheques into Pound Sterling you'll get the best rates at Thomas Exchange Global bureau de change shops. They have branches near the major rails stations in London (check online).
14) If you like to use the internet a lot, you may find it better value to buy a mobile hotspot device and a pre paid SIM card for data usage. We don't have as widespread free hotspots in London compared to many US cities. I'd recommend either the Three network or EE for 4G service.
15) A lot of the people who work in the restaurant and hospitality industry in London are from overseas. They may not be native English speakers so keep a close listen on accents (even a typical London accent may sound odd to you, lol!) and be prepared to modify your accent or the speed at which you might speak so that you're better understood.
16) Lemonade here is what you would call Sprite or 7Up (except it's only made with lemons). We don't generally drink still (non-sparkling) lemonade.
17) Iced tea is not that common.
18) Soccer is the national sport and even though the word "soccer" was coined here in England (it's derived from "Association Football") we always call it "football". Most Brits don't follow American sports to any extent, although they may be familiar with team names or certain star players.
19) Cider here is always alcoholic, made from fermented apple juice. Perry is the same but made with pears (increasingly it's just called pear cider). What you call "hard cider". If it's just plain old apple juice then that's what we call it

20) If you don't want to take one of the open top tourist bus tours, just go on the No. 11 bus - it goes by many of the major sites of London.
21) Black London taxi cabs are fun but pretty expensive, although the drivers are often very friendly and knowledgable. Uber cabs are available easily enough via their app.