Are there not any parking restrictions in the Wigmore Park car park?
If not, there should be - no need to charge, just have a maximum stay of say three hours and no return within a certain period.
Seems like the council needs to get to grips with this - and locals need to hold the council to account via their local councillors.
I have lived in places when residential permit parking restrictions have been introduced - yes, it means extra considerations in terms of visitors or tradesmen and so on - but it improved the street and surrounding ones immensely, and I would definitely recommend it.
I appreciate the park is a slightly different matter, but it needs some sort of controls too.