Removed old wallpaper - why's it blue underneath?

[BatsPigeonsRatsSquirrels]

At first I thought the blue I was finding under two layers of painted-over wallpaper was old paint, but it's got patches of different colour and I think it's something else - googling suggests people might have put glue or something else under when planning to wallpaper?
I want to remover the paper and then paint the wall. It was a particularly unpleasant paper, imo! Do I need to try to remove the blue stuff (it comes off a little bit with sugar soap but most of it is left behind) or can I paint over it? Should I use a special primer or something? I will attach pictures - including one where a bit of plaster came off with the paper so you can see the wall underneath.
For reference, it's a former local authority house built around the 60s (I think).
Thanks to anyone who replies!

I disagree. Lining paper is a nightmare if you have to do any work on the walls, replacing windows, etc., and you can always see the joins, which annoy the heck out of me. If you need a new socket in, it makes a hell of a mess which can't be patched.
With older properties with lime plaster- the plaster needs to breathe. So clay paintor limewash on the plaster is best. Wallpaper is a no-no, the paper stops the plaster breathing and paste just harbours moisture. When I've stripped the old walls here, I have to go over them again with warm water and a scouring pad (the green plastic sort) to get the paste right off. Any remaining distemper after that is just a pigment stain on the plaster, and claypaint sticks beautifully to the plaster. It's where you leave any wallpaper paste that the paint doesn't stick.
The bottom foot or so of the paper here when we came was damp. if you peeled the paper off, the paste was, and stayed, sticky. Once the paper was off and the paste was scoured off, the walls dried out. When the house itself dried out, the lower areas of paper did dry out, but when the paper came off, the paste still sucked up moisture and got sticky. Once I scoured it off, and painted it with clay, it stayed dry.

If the walls are lime, I'd stick to claypaint. If money is a problem, 'contract' emulsion- the stuff you can use on new plaster. Other modern pains are not as breathable.

"Contract" just means cheap.

If you want a porous paint that water vapour can pass through, you need a non-vinyl matt. Dulux Trade Supermatt is the best known. Other makers are likely to call their line "paint for new plaster" because it can be used on walls that are mostly dry, but still drying out.

It will not be as durable or washable as a vinyl paint.