We had something very similar done ourselves.
When we moved into our house, there was no power in the garage. I got a friend in (proper electrician) and he run a cable from the house to the garage, to provide a socket in the garage, a socket for the garden and a light for the garage.
The cable was run underground - you'll need "armoured cable" - there will prob be lots of different specs, so better to get someone who knows what they're doing.
There's a separate circuit breaker in the garage and some kind of switch/junction box inside the house, where the armoured cable starts off.