I haven't actually been to The Moor market yet - it's quite far from me but I had a little look around courtesy of google street view. As far as I can see most of everthing is covered in plastic.
I have been to visit 'Just natural' green grocers in Crookes - they had a few things loose - some of the fruits and some of the veggies but not a lot more than a supermarket might. They had some loose snacks but it was mostly sugary things like dried fruits and chocolate covered stuff. I was hoping for wholefoods such as grains, pulses, nuts and that sort of thing sold loose or in reusable containers rather than the usual non-recyclable plastic film.
So far Lidl and a couple of small green grocers seem to be the best places. Lidl stock loose almonds, peanuts, pistachios and quite a few of their veg are loose too. A local butcher said they would be happy to sell meat to me in any container I bring from home. I've bought some reusable mesh produce bags from a company called 'Onya' ('Onya Weigh' bags) and so far used them in Tesco, Waitrose and Lidl without any problem.
Hopefully this sort of thing is catching on and more food stuffs will be available without the packaging. Would love to hear from anybody else about their zerowaste purchases around the city.