London in May

We're going to London in May. Our friends who live in Ontario are coming too.

We fly out of Vancouver on the 18th of May, arriving in London the afternoon of the 19th. They fly out of Toronto on the 19th and arrive on the 20th.

We're staying in London until the 23rd. Then we're taking the train to Edinburgh and staying in a self-catered flat there until the 2nd of June. Lovely flat too I must say and quite a savings over a hotel.

But we have yet to find a hotel in London. We want to stay in Bayswater/Paddington.

I've already tried booking The London Elizabeth Hotel through the hotel club but it was unavailable.

So I'm looking for suggestions and especially for recommendations. (Comments about hotel club would be welcomed too.)

Leaving as much money in our pockets as possible is desireable so if 4 nights comes in under 400 pounds that would be good.