For lighting and a coupple of DIY sockets a 20A supply will be heaps.
You need a registered electrician to install armoured cable of the correct size between the house (mains intake point) and the garage.
A switch fuse at the house end and a mini garge consumer unit at the garage end.
Simples.
All you have to do is dig a 400mm deep trench down the garden for the cable to go in to.
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