I believe you don't have to have a helmet to ride a quad bike, so I don't see what issue that should present to the police. Standard rules about endangering bystanders though, but I think the way these things are being driven they are already a fair risk to the innocent.

Also the crazy quad bike that weaved around my car and other traffic the other night had a number plate - I don't get why the police can't stop these twerps, and if they fail to stop, just go to the registered owner and persue them. And with all the NPR cameras around London, I would have thought it would be an easy catch once their plates are registered for a crime (e.g. failing to stop, dangerous driving, speeding, driving on 2 wheels on a public highway etc).

Finally these things are really noisy - they must have knackered the exhausts which probably means the engine efficiency is down too. Do they have to pass an MOT, do they pass, and what about the Low Emmision zone? Are they even insured to drive on the highway, without a helmet, or on two wheels?

I'm sure there is more complexity than this, but these quad bike are a noisy antisocial nuisance and a danger on the roads. I expect it will only get worse as summer comes along, at least until Darwin is proven right.