2 B&B's or do you have a better place to stay in London

If your primary destination is London, then stay in London.
My suggestion:
Go to www.betterbidding.com and read the FAQs and then check the other destination forums for Priceline and Hotwire to get advice on your stay.
We used the tips from there to bid and stayed at the 4* Marriott Maida Vale (3 blocks from the Kilburn Park station: 3 tube stops from Paddington Station) for under 100GBP per night. Some have 'won' 5* in Mayfair zone for as low as $130/night +tax/fees, but more typically it is $170/nt +tf. You aren't likely to get a bad place if you go for 4* and 5*.

I agree that if you are visiting London, stay in London. Rick's books have good suggestions for a range of accommodations. We have stayed on Ebury St in a small budget place about 10 years ago and in the Notting Hill area on a later trip. The Ebury area is close to Victoria Station and the coach (long distance bus) station and within walking distance of major sites. I haven't taken the tube from Heathrow to that area, but generally it's the easiest (and cheapest) method to get into the city (get an Oyster card at the entrance to the tube at Heathrow - we found the "pay as you go" option to work well - 10 + pounds is a good amount to start with)

We just spent two deluxe nights at the brand new Park Plaza Westminster Bridge hotel, right across the Thames from Big Ben, and two blocks from Waterloo train/underground station. It's not cheap (169 pounds a night for a family of 4 -- but they do have rooms that accommodate a family, rather than having to book two rooms), and the location was superb! We could walk to Westminster Abbey and Parliament, to concerts and the theatre at the Royal Festival Hall area, and to the Globe and Tate galleries. And we were in the first round to go up in the London Eye, since this hotel is only two block away.
It's an easy two-ride journey from Heathrow: take the Heathrow Express to Paddington Station, then the tube to Waterloo Station.