I don't repot mine, but I just replace the top inch or two of compost in early spring just when it looks like it is coming into life. But mine is in my tunnel.

Repot when it is dormant either late autumn or early spring. However, if you are in southern Britain and have a sunny south facing spot, you would do far better if you grew it in the soil.
The only thing that needs winter protection are the 'embryo' figs which will make the first (and in the UK, the only) crop of figs in early summer. You can achieve this by covering the tree with fleece. They will withstand ordinary frosts but not continual freezing for several weeks.
The other problem might be, if you have very fertile soil, that it will grow too much, in which case you can line the hole with stones or gravel.
I must say we have NEVER done this and our figs have produced abundantly and quite early, but maybe our soil is very poor! Ours grows against a barn wall.