Assuming re-finishing the entire wall is right out of the question, except for a new coat of emulsion...
This might be easier if that's anaglypta on the walls rather than textured paint, but the 'fix' is about the same either way.

Use a cheap chisel or sharp wallpaper scraper to get the worst of the over-filled patches off, taking the paper or paint off for a couple of inches around each hole, let the edges tear raggedly - it hides better later.
Use pliers or whatever will fit to rip out the rawlplugs.
Fill with Polyfilla, smooth to the plasterwork.
Tear a bit of anaglypta by hand so it has feathered edges & glue into the gap.
Finish with matt paint, which will hide the joins far better than eggshell. If you're trying to match to a surface that's had 17 layers of paint since it was last papered, over-layer the new patch several times until it starts to better resemble the old finish.

Assuming re-finishing the entire wall is right out of the question, except for a new coat of emulsion...
This might be easier if that's anaglypta on the walls rather than textured paint, but the 'fix' is about the same either way.

Use a cheap chisel or sharp wallpaper scraper to get the worst of the over-filled patches off, taking the paper or paint off for a couple of inches around each hole, let the edges tear raggedly - it hides better later.
Use pliers or whatever will fit to rip out the rawlplugs.
Fill with Polyfilla, smooth to the plasterwork.
Tear a bit of anaglypta by hand so it has feathered edges & glue into the gap.
Finish with matt paint, which will hide the joins far better than eggshell. If you're trying to match to a surface that's had 17 layers of paint since it was last papered, over-layer the new patch several times until it starts to better resemble the old finish.

This is the edge of an anaglypta patch I managed to find, lit from the side so it stands out a bit more…

Assuming re-finishing the entire wall is right out of the question.
This might be easier if that's anaglypta on the walls rather than textured paint, but the 'fix' is about the same either way.

Use a cheap chisel or sharp wallpaper scraper to get the worst of the over-filled patches off, taking the paper or paint off for a couple of inches around each hole, let the edges tear raggedly - it hides better later.
Use pliers or whatever will fit to rip out the rawlplugs.
Fill with Polyfilla, smooth to the plasterwork.
Tear a bit of anaglypta by hand so it has feathered edges & glue into the gap.
Finish with matt paint, which will hide the joins far better than eggshell. If you're trying to match to a surface that's had 17 layers of paint since it was last papered, over-layer the new patch several times until it starts to better resemble the old finish.

Assuming re-finishing the entire wall is right out of the question, except for a new coat of emulsion...
This might be easier if that's anaglypta on the walls rather than textured paint, but the 'fix' is about the same either way.

Use a cheap chisel or sharp wallpaper scraper to get the worst of the over-filled patches off, taking the paper or paint off for a couple of inches around each hole, let the edges tear raggedly - it hides better later.
Use pliers or whatever will fit to rip out the rawlplugs.
Fill with Polyfilla, smooth to the plasterwork.
Tear a bit of anaglypta by hand so it has feathered edges & glue into the gap.
Finish with matt paint, which will hide the joins far better than eggshell. If you're trying to match to a surface that's had 17 layers of paint since it was last papered, over-layer the new patch several times until it starts to better resemble the old finish.