It's hard to give a definitive answer to the legal question. Driving on the pavement is an offence, although it seems to be rarely enforced. So far as I know parking on the pavement is not an offence in itself, although causing an obstruction could be. But it's a matter of opinion what counts as an obstruction. There is keeper liability for obstruction, so a ticket could be issued, but this is rarely done.
In practice, it seems (regrettably in my view) more or less impossible to persuade any authority to do anything about parking on pavements. The only effective solution may be requesting the highways authority (often a county council) to make access to the pavement physically impossible.