I will be in London in May and would like to visit a street market for shopping and maybe lunch. I enjoy going to flea markets here in Florida (you never know what you will find).
I would like to stay closer to central London, but would consider going further out.
Open to suggestions.

Depends what sort of market you're looking for, but you would get a good mix of offerings at Brick Lane and Spitalfields on a Sunday.

Some other options:
http://www.visitlondon.com/things-to...ns-top-markets
https://www.timeout.com/london/shopping/london-markets
http://www.streetsensation.co.uk/markets.htm

My day for Markets is on a Wednesday.

Spitalfields would be my first suggestion as well. They have food outlets and lots interesting stalls.

Spitalfields looks like an indoor market, good for any weather. Looks like they would also have many choices for a quick lunch.

There are some great food stalls at Spitalfields. Gets very busy with City office workers. Some food trucks outside as well. And regular restaurants too. Or go the the Ten Bells Pub opposite.

If you enjoy flea markets for the thrill of the hunt (vintage bric a brac, etc), Spitalfields may be a bit disappointing. On Wednesdays, it may be mostly a food market. It's a fascinating area and well worth a visit but may not allow you to scratch the 'flea market' itch. I'd suggest Kempton but that is only second and last Tuesdays and Kempton is not central London. Portobello has antiques on Fridays though Saturday is the main day. Camden Passage (NOT Camden market) has interesting stalls to poke around in - and main market days are Wednesday and Saturday so that might fit the bill.

From the pictures I found Camden Passage looks like the type of place I would be looking for. It too seems to have interesting places for lunch

For me Brick Lane was underwhelming. Very nice area though.