Short answer: yes, it's possible — but nine times out of ten I'd strip it. Painting over wallpaper is a shortcut that often bites you later, so let's be honest about when it works and when it doesn't.
The big risk is moisture. Water-based emulsion soaks into the paper and the paste behind it, and that's exactly what loosens wallpaper. So a paper that's clinging on fine right now can start lifting, bubbling and peeling at the seams the moment you roll wet paint over it. Once that happens you've got a far worse job than if you'd just stripped it at the start.
- Lining paper or woodchip that's rock solid, well-adhered, with no lifting seams.
- Older painted-already papers in good nick where stripping would damage soft plaster underneath.
When to strip instead: anything textured/embossed (the pattern grins through), vinyl or washable papers (paint won't key to them), or any paper with lifting edges, stains or mould.
If you do go ahead, the prep is everything. Knock back any loose edges, glue them down, then seal the whole surface with an oil-based or shellac primer — Zinsser Cover Stain or Zinsser BIN — rather than water-based primer. That seal stops your topcoat soaking the paste and also blocks any pattern or ink bleeding through. Skip this step and you'll regret it.
For the topcoat, once you're sealed and primed you can use whatever you'd normally choose. A forgiving matt hides paper texture and seams better than anything with sheen — something like Farrow & Ball Estate Emulsion in Cornforth White, Little Greene Intelligent Matt in French Grey - Pale, or a warm neutral like Setting Plaster if you want a softer feel. Avoid eggshell and silk finishes — they catch the light and show every join.
Mate, my honest steer: if the paper isn't a struggle to remove, strip it, make good, and paint onto plaster. You'll get a far better finish and you won't be redoing it in two years.