What's the best way to find an apartment for a three month stay in London?

I'm taking my 12 year old daughter to London for three months and need to figure out how best to accommodate ourselves.

The most important aspect is that it should feel like a home, not a hotel. A studio might be okay, but I've found two places with mezzanine bedrooms or small single rooms off a main studio that are going for around £4000 for the duration.

We need somewhere furnished and with its own kitchen as I couldn't cope without being able to cook our own meals for that length of time. Unfortunately many places set up for two people have only one bed, we need two, although we could tolerate one of them being a sofa bed.

Location is not extremely important, but ready access to creative (theatrical) communities would be great, so I'm concentrating on areas in the east and west ends, or places with a direct tube link to them.

Any advice on finding the right place gratefully received.