7 day stay in London

We stayed at Kildare Gardens Bed & Breakfast which appears to be in your price range. It was conveniently located near Nottinghill and Paddington Station. On a quiet cul-de-sac but near shopping and restaurants. They have weekly rates. I just googled to find it.

We stayed at this place in South Kensington a few years back: http://www.darcyaccommodation.com/2008/04/24/wetherby-place-south-kensington/
It was very nice, close to the Gloucester Road metro, lots of restaurants and pubs, etc. It's a little over your price range but not much. Apartments are a good alternative to hotels for a weeklong (or so) stay. You get more room to spread out, a kitchen to save eating cost, often a laundry (the one above has), maybe also a more "authentic" neighborhood where you feel more like a resident. (Though, as someone noted in another post, the residents go off to work every day while you go to the museum or café or whatever!) Pay attention to what floor it's on (remembering that first = our second) and whether there's an elevator if relevant. Terms like "king size bed" may only mean what we'd call a double, clarify with actual width measurement if you care. Plumbing and appliances can be, shall we say, an adventure (we were lucky that our oven shut off automatically after an hour because we couldn't figure out how to do it). There's no front desk or concierge to look after you, but there should be a local contact person (not necessarily the owner) to respond to problems. We've had good experiences renting through homeaway.com in Europe and US. I don't know the agency whose website is above, only the apartment. We rented it through some other outfit that I don't recall now. You may be too close to late August to find a good place now, but give it a try. Happy anniversary!

This link is for a set of guides/advice (including budget hotels, apartment rentals, pubs etc) from Tripadvisor, it is supplied by a regular US visitor to London. It has some very good info. PS - unfortunately the link did not work but another way to get to the info is to use the link in the first post on this TA thread http://www.tripadvisor.co.uk/ShowTopic-g186338-i17-k6625083-Triple_rooms_in_central_London-London_England.html#50897052

Our family rented through A Place Like Home and the apartment we had was exactly as advertised. The company was easy to deal with and it worked out beautifully - I would definitely stay in one of their apartments again. Since that trip, we've stayed in a number of different hotels (since we were only in town for a few days) - recently stayed at the Ashburn Hotel in Kensington and would definitely recommend it - our room was small but very well appointed, quiet and the staff was quite helpful. Personally, I love renting flats and generally prefer them over hotels. I find that even with a studio, you end up with a bit more room and we like being able to have dinner in if we wish - definitely helps with the budget! Marks and Spencer, Waitrose and Sainsbury all have pretty good ready - to - go meals which make a nice break from eating out every evening. As others have noted, perhaps the only downside is the lack of a concierge - but given there is no language barrier and London is so easy to navigate that may not be a big issue at all for you!
We love London and try to go every 1 - 2 years so if there is anything else I can help with, let me know!

We stayed 5 nights at a flat and its hard to beat the price. Very centrally located to everything and close to a major tube stop, restaurants, and a grocery store. The owners are very nice and helpful. I would stay here again! I have the owners phone number. Let me know if you are interested.

I looked for flats vs. hotels in London for a week at Christmas last year. Yes, a flat would have more room and provide kitchen if you want to eat in. However, we enjoy eating out in London at pubs and other reasonably priced places. For 5 days you don't need laundry. We stay at the Rembrandt and book through British Airways in conjunction with air travel tickets. A wonderful hot buffet breakfast included. However, it is probably a bit above your price goal. But, the point of all this blather is that I found flats, unlike in Paris, to be no cheaper on a daily basis than the Rembrandt.