Yes, it's Artex... virtually impossible to repair and get a decent match to the pattern.
Worse yet, it contains asbestos (unless it's very recent), so removal is a specialist job.
Plastering over it it probably the cheapest option, but masks the problem rather than solving it.
looks like it's been finished with a foam paint roller, you would have to get the mix just right to match it, even then it would take some blending in, plaster overskim would be best, as already said?
Having done some more research and asking, it seems to be just Artex with a stippled finish, so I've bought a repair kit and I'm going to give that a go and see what happens. I can always paint over it afterwards so it's less obvious