I'm thinking of getting a Dremel or Dremel-like rotary tool for taking
stubborn things apart, improvising spare parts, making a mess, etc.

Among other things, I've seen some sets at Maplin in the £25 to £32
price range (their codes N52FX, N14BG, N60GR), but I don't recognise
the brands so I wonder if they're any good. A genuine Dremel 8200
from screwfix.com is £100.

Comments on brands & quality? Other recommendations?

Are the blades & such interchangeable between brands?

I see that the Dremel 8200 only comes with one battery, but it's a
Li-Ion, so that shouldn't be a problem, right?