Apartment / hotel with 2 singles beds London

[Lazydaisy991]

Can anyone recommend apartment in London for 3 nights for 3 adults and 1 child. But 1 double and 2 singles, Child is too old for uncomfortable pull out sofas
Budget is ideally £250 - 300 per night.
Somewhere easy to get to sights,but doesn't have to be bang in the middle of London but also prefer not to have to travel by train to get into town.
Or else a hotel with 2 singles as a twin and interconnecting rooms

Hi, probably too late now but we stayed in the City Sleeper (an Imperial Hotels brand) near the British Museum last summer. It cost £320 for the night for the pair of interconnecting rooms with breakfast buffet. The rooms overlooked a busy courtyard with car drop-offs and people eating/drinking and was quite noisy even with the window shut so I bunged my earplugs in and slept adequately. It's not ideal but at a pinch I might stay there again. (I am a very light sleeper). Nice bedding and bathrooms. My teenager slept in the other room without needing earplugs.