There is an excellent butcher in Adel, on the northern edge of Leeds, who will get you any meat you ask for, within reason, on request.
There are also 3 very good butchers I use, all halal incidentally, that sell goat as a matter of course (on or off the bone). You can throw a blanket over them on the Wetherby Road between Harehills and Oakwood for those that know the area I suspect many people don't know just how friendly these places are. They are staffed by smiling people who don't mind you asking questions; for example, they don't have a whole leg of lamb on show but if you ask for one they will go out back, which you can see, and cut you one for at least half the price of Tesco which is only about 200 metres away.
And yes, I suppose I am lucky, but there are of course good and bad points to living in Leeds. Access to great local shops is one of the good things.
Where I live the butchers are fairly poor. They all seem to offer cheap sausages, chicken and burgers in BBQ packs and little else. We have a farmers market that comes around every so often where you can pick up some good quality meat and it is almost as cheap as what our local butcher charge for cheap rubbish. I've heard him moan about the farmers market because it is ruining his business.