Daisy - one thing you are not doing is overreacting to this.
Years 3 and 6 'playing' together with no effective supervision raises questions for starters. That is a big difference in age, size, etc.
Take photographs of the injuries, now and over the next couple of days (so you can use the worst ones).
Start a paper trail. Everything in writing. Get your ds to go through what happened and between you write down what he says - when, who, what, how he felt. Start to keep a record of everything he says has happened since the start of term.
Contact the Head in writing to say you want an appointment and why. Follow up the appt again in writing. I don't know who 'the school' is who you have talked to so far. If the Head is no use, then governors, etc. But everything logged and in writing. Look through the anti-bullying policy (which I, too, would love to see, especially the bit about the bullies having to admit it!) and look for the buzz words: safekeeping, loco parentis, right of the child to feel safe, etc, and quote their own words back at them. Good luck.