Hello, thank you for your question.
Depending on the layout of the road/ driveway and the number of people that have access this may still be classed as a "Public Place" for the purposes of Road Traffic legislation. If so, then these issues are criminal and you could report them to the Police if you wished too. Even if you are unsure then you could always try phoning 101, some forces are more helpful than others and you might find that a constable is willing to go and have a word with him even if he is only driving on private land.
I note that your concern is that you might be liable in the event of an accident. I don't really understand why you would be worried about this. As a general rule you can only have a civil claim brought against you if you have done something wrong. So if he crashed his bike, you would have to have done something to have caused him to crash. If you'd left a load of gear out on your driveway and he crashed into it then maybe you could be liable, in the same way that if a pedestrian fell over it you might be liable. But, if you are leaving the right of way clear, then you aren't doing anything wrong.
Is there a particular reason why you thought you might be liable in the event of an accident?
If your concern is about the noise and that being a nuisance to you then you could look to obtain an injunction to stop him riding excessively up and down. then you can get some useful tips here: https://www.gov.uk/how-to-resolve-neighbour-disputes/take-action-through-the-courts. The key is where possible try not to escalate things as neighbour disputes regularly get out of hand.
Ultimately if none of this works then in theory you could apply to the courts for an injunction but these are complex applications and can be very expensive indeed.
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