What you will have to watch out for is an Out-building with a footprint of over 30m2 will need planning. 20'x20' comes out at just over 37m2.
16' x 20' will give you just under. The roof line must be under 3m (10') and the building must be constructed from mainly non combustable materials i.e brick/block roof tiles etc
I'm in the building game if youre wondering how i know this, and i'm an Essex boy so just across the water.
If you're gonna go through planning call it a Summer house not a Studio otherwise they might start with the "Are you running a business from home" and you'll be in a whole other ball game, but thats your call
Hope this helps in some small way, if not just ignore it
Be interested to know how your getting on, as i'm in the middle of constructing a LARGE Summer house as we speak!
Take care