Arbutus unedo (common names: Strawberry tree)

I think you should wait until Spring, but I expect there are flowers on it at present, mine is for the first time, and possibly fruit, which takes a year to mature, So you have to decide whether to prune or to fruit. You live in a lovely warm part of Hampshire . I envy you ,,we are quite cold up here near Basingstoke and And Hook..

We destill the fruits into a very potent drink - here in Greece...

Here the trees fruit and flower almost all year around, depending on how much sun they get (they grow wild here) ... you can prune in stages to give it form - nothing too major at a time, also nipping the tips will give a bushier grow. Give it sun and not too many nutrients in form of fertilizers, but rather leaf compost.