My pal, GretchenS, from the Home Cooking Board gave me the heads-up on this place. She'd visited years back and rated it highly. It's a small shop and the cheese range is limited (far less than, say, the Cheese Shop, in Chester), but its produce is of high quality. You'll find some of the big names here - Montgomery and Keens Cheddar, for instance. But we asked what they had that was local and were pointed towards the Anster (http://www.standrewscheese.co.uk/)
And they'll sell you the bread to eat with your cheese - fresh seven days a week.
Apparently they have three branches in the city. We visited the one on Victoria Street, just near the Castle. Certainly worth a trip, even for tourists like us, for a foody souvenir (even if one that's only going to last a day or so.)