There’s a private road in front of our house. We are responsible for its upkeep, and properties further along have access rights. Can non-residents use our road as a car park? We often have to leave our cars because the road is cluttered with other people’s vehicles.
If you own the road outright and other residents merely have access rights (and hopefully maintenance duties) you can probably put a locked gate at the end to prevent non-residents parking along it. You would of course have to give your neighbours keys. Double-check your deeds as regards ownership of the road. If you each own just the stretch in front of your houses you will probably only be able to act by unanimous agreement.