I already had half a reel of three core round 2.5mm round flex in my garage.
I used a single ( to save on space ) weather proof outdoor socket outlet from Screwfix.
Because they sell more of the double type, the single outlet is a similar price.
I just wanted to keep the size down to a minimum.
I terminated the cable with a suitable weather proof gland at the socket outlet.
I used a M.K. three pin plug with a 13 amp fused installed of course.
You can get away with using a 1.5mm cable ( but no smaller ) and 2.5mm could be seen as being a “Bit Over The Top”.
But I had it already and will have handle the load with ease.
Of course, you have to be comfortable doing this type of work.
I also have a boot ferule kit that allowed me to terminate the single conductors correctly at the socket outlet, because the round flex / cable is of the multi strand copper type.
The ferule kit is not essential, and not totally necessary, it just makes a better job really.
The only issue I had, was because the three pin plug on the “Granny” is a little baulky, I had to trim the enclosure slightly in order to get the weather proof lid to close and seal correctly.
Looks a bit like like this !.
View attachment 3139