Use light weight spackle, such as Red Devil "One Time", to fill the grooves. You can tell the light weight from regular spackle because the container at the store feels like it's half empty. Becuase very little liquid is used in it, it doesn't shrink nearly as much as joint compound. It should fill those grooves in 2 applications.
Use new (sharp) sand paper to sand it smooth, as dull sandpaper doesn't work well - you need the cutting action. 120 is a good grit to use.
Prime, paint, admire.
Not sure but I'm guessing in UK they have something similar but of a different brand.