Tyres are not just made of rubber, they contain lots of bad additives that you don't want anywhere near your food crops.
Bob Flowerdew addressed this criticism on a recent GQT. He acknowledged that there was some concern but from his research concluded that there wasn't a significant problem. He uses old tyres extensively.
Bazz, unless the site rules prohibit tyres there's nothing to stop you using them, though you'd actually need to be seen to use them; every site should have a rule about accumulating rubbish so if they're not being used you'd have to get rid of them.
Tenants leaving their crap behind certainly is a problem and tyres are expensive to dump so it's not just a question of the committee going in and clearing up at just the cost of their time. But you have to balance that against the legitimate right of the tenant to garden how they want.
Tyres can also be used for building but the problem of clearing up at the end of the building's life put's me off a bit, but then getting rid of anything you can't burn is a problem so I'm still interested in the potential of using tyres like this.