Not sure, but I think the Headingley farmers market is on a Saturday. mapleleafgirl72 will probably know. Also, I'll see if I can get HME to pop in on this thread cos I know she knows for certain & also will know where the green grocer(s) and other cool places are - she knows everything! 
We went to the Headingley farmer's market yesterday and found a few lovely things. But it's only once a month and quite small--there was one veg stall with very basic things and one stall with strawberries, and the rest was pies, jam, cheese, etc. Nice for treats, but not really my idea of a farmer's market, and not somewhere that would help with my regular shopping.

I've figured out where the greengrocer is, but haven't made it there yet.