I had a c-section at George's and was out the next day. They run a programme called enhanced recovery which aims to get you on your feet, everything having gone well, the evening of the op.
With a planned c-section I don't see why they would keep you in, it's only an emergency where your body has been under extra tea strain etc
As above, being at home is far better than being in hospital especially if you are in a shared ward.
At George's you can ask for a private room which they'll give you if available.