I thought about doing that here, but the problem with that is that when the butts suddenly fill up is the time when you don't need to do any watering. So I've got a manual diversion system for the kitchen waste water which gives me about 4-6 buckets of grey water a day for the garden. Any other garden watering is verboten in drought periods.(Note - the water is distinctly 'whiffy', so the butt needs a lid to keep neighbours happy.)
It would be a different matter if the butts were big enough to hold a few weeks' worth of water for the garden, but(t) most would only hold a few days' worth (which is better than nothing, but not enough for any proper drought).
Rather delightfully, using my 'grey water' daily has saved a blackcurrant bush which looked as dead as a doornail when I arrived, the bay has perked up, and the gooseberry might *just* survive. I don't bother with fancy watering cans – a good bucket drenching does the trick.