Patches show on wall after paint matt dries.

This could be to do with the plaster balram, when a wall is plastered to the "polished" look, it can make it a nightmare to paint. I'm not sure if it was a freshly plastered wall but if it was then your best bet is to white wash the walks first in some watered down paint

I would wash walls with sugar soap then line walls with 1000 grade lining paper paint wall 2 coated of emulsion

Difficult without seeing the job but id suggest getting a decent roller, make sure you load it with a decent amount of paint. Roll in a M motion overlapping each run. Dont try and cover too much wall with each load. If you are struggling with uniformity still do a second coat and dont assess it for a couple of days, give it time to settle.

Hi, Painting white on white can be quite tricky. From what you have explained, it sounds like you have just given it a blow over with a fresh white matt...You did not mention what if any action you have taken to prep the wall prior to painting. The end result regardless of colour is all in the preparation...Always give the wall a good sanding after filling any holes/cracks and give it a good clean with sugar soap or at least sponge it down with a damp sponge and allow it to dry before painting, Always apply a min of 2 coats allowing each coat to dry before applying the next one. Also, the quality of paint is key...Alway's go for a quality brand such as Dulux, Armstead trade matt emulsion, as the opacity is often much better than of the shelf matt emulsions.....Also, you may be painting over a silk emulsion which will look poor, because the matt emulsion will not adhere properly to the surface of silk emulsion...Without seeing, it is difficult to say, but likely down to preparation, or poor quality paint....Let it dry, keep coating it till you have a consistent coverage, that will sort out any patches or flashing, keep the roller wet, don't let it dry out, paint roughly 1 M2, at a time, and dip your roller again, don't be shy with it, get plenty on the roller...