National Express said the coach was its 777 service travelling from Birmingham to Stansted Airport with 33 passengers on board.
Television pictures showed the coach on its side at the entrance to the service station.
Thames Valley Police said the coach had clipped a kerb and rolled onto its side at around 4 pm (local time).
The injured have been taken to hospitals in Milton Keynes, Northampton and Oxford.
REUTERS PY VC2350