Don't make the mistake that my American friends (and every other American makes) made when they came to visit us last year, which is trying to visit as many different things as possible, and also trying to plan multiple day trips out of London.
You're only here a week, pick a few MUST SEE things and take your time. London isn't going anywhere, you can always come back!
For me, here are a few things they really enjoyed and wished they'd had more time to really experience it:
Churchill War Rooms - the bunker complex beneath Whitehall that was used during the second world war. You need at least two hours.
The Tower of London - again you need at least two hours, three is better.
Tate Modern - depends on the exhibits. But if you're interested in art its a good place to visit.
Imperial War Museum - for me the most interesting museum in London, especially the Holocaust exhibit. Budget half a day. Free entry.
Borough Market for food - lots of free samples and you won't be disappointed.
Covent Garden for food and interesting shops. Also consider the Camden Brewery tour if you like beer.
Also, the weather in July in London will be HOT. Walking around London in 30-35°c heat and humidity is not fun. Pack a thin rain coat and umbrella but you won't need warm clothing, except maybe a hoodie just in case.
