The driver has not been driving for too long and wasn't aware of changing the vehicle's log book address
It's not the driver who needs to change the vehicle's V5C, the registered keeper does, as it their name on the document. If they haven't already, they should do this immediately. It is also not the driver who UKPC are writing to, as they have no idea who was driving, it is the keeper.
Looking at the specifics of the case - the breakdown could give rise to a potential defence of 'frustration of contract' - an argument that the terms of the contract (i.e. to not stay more than 3 hours) could not be complied with due to a factor outside the driver's control, namely that the car broke down. How viable this argument is may depend on the circumstances. If they entered the car park knowing their car was faulty/about to break down, it might be more challenging to argue that this was outside of the driver's control.