On walls I would usually use Gardz which stabilises the surface, then emulsion. SOmetimes with bathroom you might want to use an oil based eggshell although that has wained in popularity, in that case I would use a primer like 123+ and maybe and undercoat from the same manufacturer as the eggshell too.
It looks like chalky paint/filler under the paint so gardz would be my first choice but 123+ is bootstraps in this case anyway, just more expensive and time consuming to apply.
On walls I would usually use Gardz which stabilises the surface, then emulsion. SOmetimes with bathroom you might want to use an oil based eggshell although that has wained in popularity, in that case I would use a primer like 123+ and maybe and undercoat from the same manufacturer as the eggshell too.
It looks like chalky paint/filler under the paint so gardz would be my first choice but 123+ is bootstraps in this case anyway, just more expensive and time consuming to apply.