They become aggressive, call the police.
This is common law nuisance and obstruction. It’s a private lane so the police will not be interested.
It is a nuisance if it is literally, in the normal English dictionary sense of the word a nuisance. It is.
It is obstruction of your right-of-way is the obstruction is substantial and I think that in view of the burst tyres, he would struggle to prove that this parking was not obstruction.
You can apply to court for an injunction (having first threatened him of the pending application) to prevent him parking there and to us the court to award costs against him in respect of the application. To support the application you are going to need photographs and measurements of the width of the lane and how much is being taken up and how much is left and the width of cars and how the damage is caused on the stones. If you have photographs of the damage, so much the better.
The solicitors letter would hopefully avoid the risk of going to court but sometimes, people like this think they are above the law. If he simply ignores it, you are faced with taking him to court to get that injunction. If you get the injunction and he continues to park, then it does become a police matter because he is in breach of the injunction and hence, contempt of court which is a criminal offence for which he is liable to be arrested.
If several of you fund any litigation, it will divide the cost although anyone who doesn’t contribute will still get the benefit of your litigation.
Your partner needs to report this accident to the police and must do so within 24 hours because to fail to do that is a criminal offence. It carries an endorsement points. If that time is running, call the police now. It’s important to get it on the record. The police will not be involved unless the neighbour reports it but he may just be a smarty-pants and do it. If he does it, irrespective the incident, the police will expect your partner to do it.
If he claims for the cost of the damage from you, counterclaim for the cost of the two tyres.