Changing schools would be them winning. If I was the OP's parent I would write to the headmaster, noting in the letter that I was copying it to the chairman of the governors and the education chief at the local authority.
to be honest, unless that is the only school in the area, i wouldn't consider leaving as letting the bullies "win", provided they were sanctioned appropriately. The school should have safeguarding in place to ensure firstly that this should never happen in the first place, and secondly that they have a plan of action to deal with it. Assuming they dont have either, based on their performance so far, I would say that it isnt leaving the bullies, its leaving a school that is not able to properly care for their students, something by law they must do, so get out now!