It looks like it’s a Grohe. Grohe do parts, also for their older models, but there is a cut off point I think.

I’m no expert but if you want a nice clean finish it’s best to get a plasterer to skim the walls. You could try some filler like Polyfiller in the dips, let it dry hard then gently sand smooth.

you will protect the timber better stopping the paint on the mastic line, so if you apply a line of tape in the mastic you will get a straight line to finish the paint against. stopping at the mastic joint can expose the back of the timber to the elements. if it was not primed and painted when being installed, which is not generally the case, it will be more prone to water penetration and ultimately rotting. hope this steers you to pick the right solution. aesthetics are important, but protecting the timber is the number one reason for applying paint. best Rowland

Email the BBC? It looks like Oval Room Blue but impossible to be truly sure.