Just to follow up on this in case anyone is doing a search in the future.
I phoned the Observatory and they first insisted on refunding the cost of my ticket as a carer
. They also booked the wheelchair bay for DH in the planetarium, which has a great view although you miss out on sitting on one of the laid-back seats.
Parking-wise, there was absolutely loads on Blackhealth Avenue. We got there at 11:00 so not even early. The Observatory lady had said there probably would be parking even though the car park was small (I assume she meant another car park as by no standard could this be called a small parking area) and expensive (4.80 for 4 hours? That's not expensive for where it is).
Anyway, the Observatory site is quite challenging for a wheelchair user. Cobbles and lots of rather narrow corridors. The camera obscura is not accessible at all (no indication of this in the map) and there is an outside lift to access the Flamsteed House, which was fine - you just have to ring to be let in through a locked door on the upper floor.
You certainly couldn't also visit the lower part of the site, where the Maritime Museum is, without re-parking as there's a massive, steep hill in between. I can't see any info on parking at the lower site on the website.
All in all a reasonable visit, not the greatest but not bad.