Our abattoir slaughters on a Monday, the butcher butchers on Tuesday and Wednesday. So our options for hanging are <24 hours, 8-9 days, 15-16 days.
We always ask for 8-9 days for mutton, prefer same for hogget, don't mind if the butcher wants to butcher lambs the next day (but happy to hang for 8-9 days if butcher not strapped for space.)
We ask for 15-16 days for cattle 1-2 years old, ask for 3 weeks for older cows especially if fat, but don't usually get it.
The busier the butcher is, the less keen on hanging they are.
Having had occasions when we didn't get meat hung for as long as we wanted, I'd say it's made no appreciable difference to taste but the meat from older sheep can be less tender. Well-hung mutton melts in the mouth and chops don't need the long slow cook, they're just as tender as lamb even when cooked fast. If the mutton didn't get hung for 8 days then the chops need to be roasted (not too quickly) with some fluid, will be a bit chewy if fast-griddled.
But, before I arrived here and they just had Zwartbles (and Dexters), they never asked for the meat to be hung at all, and it was all very tasty and the lamb and mutton perfectly tender enough. Maybe not quite as tender as our mixed breed sheep meat now we have it hung, but not tough.