Hi, I had purple suede effect on my wall. Easy to sand the texture off. Talk to your paint shop about the right colour undercoat/sealer to cover a dark colour before painting your new colour on with 2 coats.

I agree with both your painter and your Google result. The issue is something that has soaked into the surface of the old wall, particularly as you had an odd result when cleaning. You can’t expect the painter to sand and paint as part of the original job but they may be able to offer advice and action if you’re prepared to pay them. If you want to DIY I’d be sanding the wall and trying some stain locker undercoat.

The best way to cover dark is to use a grey tinted primer first. Talk to a paint specialist. Dulux on line may help

quite possibly, that was going to be my next solution! heading back there in a moment to check it out. the existing tiles have been layed quite nicely/flat so i dont think tiling over would be an issue