Is the problem only in the bathroom? Have you checked in the loft? you may find that the insulation could be soaked due to roof slates missing ect.
I'll second that,
First get up there when it's daytime and see if you can see any daylight,
Check all the felt, make sure none is dangling down,
Go outside and up the ladder (you don't need to get on the roof) and have a good look to see if any tiles are loose,
Check all the gutters and if needed clean them out,
Check the ridge tiles are all pointed up,
If you can't do ladders borrow some binoculars and look from across the road,
but the main one,
Ventilation in the loft and the soffits ain't blocked up and there's a good flow of air,
But the very main one;-
INSULATION !! and lots of it tucked in and no gaps. Don't have one inch of exposed plasterboard showing in the loft. Cold air and rising warm air with no insulation will cause mould like that in your pics.
I had this exact same problem but not to the extent of yours in a bathroom. It was the shower and extractor fan and not enough and missing loft insulation. I changed the fan to a better one and even open a window and loaded the loft above the bathroom ceiling. I even got some mould in the bathroom, that was insulation.
If you do all the above and bleach spray it will go