I would think there are school govenors so you could ask for their details and make a complaint to them.
The school itself must also have a complaints' procedure - although true, it is probably for complaining about teachers and other students' behaviour rather than the school expansion strategy itself. Still, worth thumbing through.
You could also group together with other parents and put pressure on. Call a meeting externally through your class rep groups.
Decide a plan of action: state your demands.
Go to the national press....
I guess you're not going to make yourself popular with the head by doing any of this! But then perhaps you've gone past the point of caring.
You could also talk to your local MP and ask for their thoughts. Sometimes they have some interesting angles and will also know more about property ownership, the movers and shakers around the borough, what's going on generally.
I find it an odd thing to do. Surely they'd have a natural flow of kids coming up from multiple primary schools within their network. It would appear they could easily fill their places. But perhaps that assumption is incorrect. Maybe not enough people had filled up the spaces offered at Battersea?
Perhaps the first thing is to ask for a face to face chat with the head to find out why this has happened. Honesty on their part may go a long way to explaining this decision.
If I had a child there, I would be furious and feel very let down. People have made decisions in good faith and then been thrown to the wind. It's not what you'd expect from a brand like Thomas's.