Peeling paint on ceiling

misa.blue

Hi Everyone,

we've been in our house a few months now and are attempting to decorate the hallway. The paint on the ceiling has peeled at the edges leaving a chalky residue underneath. We've removed all the paint from the ceiling using a scraper and most of it came away ok but there is this dusty coating remaining. Have bought some stabilising primer recommended from a diy shop (Zinsser Bullseye 123) but that just peels straight off too.
Any ideas what we should be doing. Should we just add some more coats of normal Dulux and hope for the best.

Also, lower down in the hallway there is a section where a couple of layers of paint have been removed from a wall, about a couple of square feet. What's the best way to even this up for a decent finish. Was thinking drywall mud but I'm not the best at diy. We're hoping no-one is going to say we needs the lot sanding down.
Thanks in advance.

misa.blue

Forgot to say the house is late 60s so we're guessing it's not calcimine on the ceiling.