Your best bet is AirB&B. When we had our house refurbished we had rented through Foxtons short let because at the time we didn't know AirB&B.
I will send you a PM as we rent our house out occasionally!

Hi there,

We currently live in Battersea and are having our side return done over the summer. Does anyone know of somewhere to rent for around 8 weeks from the start of June? We can be relatively flexible on dates. Ideally looking for a 4 bedroom house in the Battersea/Clapham/Wandsworth area suitable for two children aged 2.5yrs and 1yrs old. We are both non-smokers, have no pets and would be really respectful of someone else's property.

Any suggestions welcome.

Thanks so much.