Broadway Market is really special. Beautiful bohemian atmosphere with several veg options (try Vegie Table or Gujarati Rasoi). Vegan deserts/treats available plus loads of other veg friendly stalls. There is one that makes the most beautiful salads with several vegan options. Lots of fresh fruit and veg. Books (3 of the best books stores in London), records, arts and crafts and a surrounding of nice cafe's (including a Vegetarian tea/coffee house) and bars. There is also a really nice beer and wine shop who will help you with finding Vegan options and some not bad little health food shops.
Avoid the temptation to by bread and instead walk through London fields to E5 Bakery...I have tried almost all the bread at the market and none can compare. Get there early though! I wouldn't get to the market before 10am as there won't be much happening yet. This market is a community interest company that reinvests all of the profits back in to the Hackney community. Also opportunity for a lovely walk/sit down on Regent's canal which is one of my favourite aspects of London.
I would like to mention that this is not actually a farmers market so a lot of the produce is local at all. Try Teds Veg (ask which items he grows on his farm in Lincolnshire) and Chegworth Valley (from Kent). They both use natural growing techniques without chemicals but are not 100% certified - which is fine by me as long as it's natural. There are other great local merchants though for things like jewellery/pottery etcetera.
Cons: loads of in your face meatiness , can get very busy in the early afternoon