Pruning summer flowering Jasmine

I live in Brixham, Devon, and have a sunny south facing garden. I have a summer flowering Jasmine (white flowers with a lovely scent), which has been flowering all summer and has just flowered again. Trouble is it is on a rotten trellis/arbour which has partially fallen and needs replacing. When would be the best time to give it a hard prune? All the info I have says now, but it is constantly flowering