I’d defo block it in with a couple of your own vehicles, the owner will then have to speak with you to remove their vehicle.
As its parked on private land the Police effectively cannot do anything, my brother had a similar incident with a parent parking on his land to collect kids from school so he blocked them in.
Said parent came round and asked if he would move his car, he basically told them where to go and slammed the door in their face.
About 1.5hrs later he gets a knock on the door from some Bobbies ,he explained the situation about it being private land and how parents repeatedly parked there.
They politely asked if he would move his car and they would have a word with the school.
Some people are just ignorant d!cks.