Appeal.
Or send proof you had right to park and to take to court if they won't cancel.
I once parked in a industrial estate which has 1hr parking on match days and 2 hours on non match days.
I was 1 hr 2 mins and returned to fine set after 61 minutes.
As did 12 more cars in the row.
The man said he couldn't reverse them after being written even though it was their mistake.
The company said the same and I must go through proper appeal channels to get the fine reversed.
Myself and 7 of the other cars all sent identical emails stating to take us to court if they wanted to enforce the fine.
8 years later and I've had no court date 
This may be slightly different if there were machines to type in reg but it still stands if you've purchased to park they have to prove by you not registering the car you've disadvantaged them financially in court to get payment enforced. This is because private parking is civil case not a legal case.
A few years ago we had a prom in local hotel and we had to drive through the car park.
Every parent got a fine and the hotel contacted the private company and got them all reversed as we didn't park.
It can be done. They don't need to enforce payment but some think if they are insistent you'll give up.