I would like to run mains to this garage, to supply lighting and light
power. I only intend this to be for 'domestic DIY' power, no plant
machinery or anything like that.

A quick check shows that 4mm should be fine for a 32A radial with cable
length of 20m. This should be run off a separate MCB at the consumer unit.
Probably best on the non-RCD side.

You need to decide on earthing arrangements. A TT might be suggested in
these circumstances as it is really a separate building far from the house.
This requires you to isolate the earth on the cable at the garage end. Then
use a whole garage RCD and an earth rod.

Best is a 100mA Type S for the entire supply and a further 30mA immediate on
the socket circuits. However, you might not bother and just use a 30mA
immediate for the entire lot. Obviously, this cheaper option would mean you
lose lighting when the power trips.

Christian.