This ^
When we moved to this city 30 years ago we were surprised that everybody parked on the pavement. Our new neighbours explained they you had to park on the pavement to allow emergency vehicles and bin lorries through. The pavements are plenty wide enough to ensure that wheelchair users and pram pushers are also able to get by unimpeded.
And as in your case there is nowhere else to park - the whole area is like that.
We've lived opposite a NHS hospice for 20+ years and on that side of the road people park with all four wheels on the pavement. It's never been an issue for all the wheelchair users who use our road. If it had been, I'm sure we'd have known about it.
A lot of people don't seem to realise that parking wholly or partially on a pavement does not necessarily mean that wheelchair users and prampushers must automatically be obstructed or inconvenienced. It ain't necessarily so - it depends on the circumstances.
When a blanket ban on pavement parking was introduced in London (in 1974?) it was acknowledged that one size does not necessarily fit all by allowing local authorities to permit pavement parking in specific areas. Obviously such permission is only given where necessary and where it won't obstruct or impede pavement users.