Paint on bumper chipping. What to do?!

Hi all. My Fabia was bought as a former cat write off which has been poorly repaired. Although everything is as I should be mechanically the bumper is messy to say the least so I'd like to try and tidy it up a bit.

Presently the bumper looks like this around the number plate:

Other than the fact the bumper is clearly lower on the driver side that the passenger side the paint is chipping quite badly around the number plate revealing what looks like a grey plasic underneath. The only way I can describe it is it's like rather than being painted onto directly the bumper has some kind of extra layer almost like wallpaper, which is now flaking off.

I'm unsure about just painting it like I normally would? Any suggestions? (Would like to avoid a new bumper but realise this could be the easiest option)