Borough market http://www.boroughmarket.org.uk/

Spitslfields http://www.spitalfields.co.uk/?utm_source=vs&utm_medium=web&utm_campaign=vs

Columbia flower market http://www.columbiaroad.info/

Petticoat late http://www.londontown.com/LondonInformation/Attraction/Petticoat_Lane_Designer_Fashion_Market/82c9/

White cross Street market
http://www.inlondonguide.co.uk/london-street-markets/whitecross-street-market.html

To get you started...

Couple more

Leadenhall market http://www.leadenhall-market.co.uk/

Camden markets http://www.camdenmarkets.org/

Camden markets are perhaps the most popular markets in London - on weeekends I believe but a real show in many ways. Right by a Tube stop - can't go wrong there. Walk a bit along the canal whilst there.

Sunday UP Market
http://www.londontown.com/LondonInformation/Sights_and_Attractions/Sunday_Market_at_the_Old_Turman_Brewery/96f0/

Borough is our favorite combine it with a visit to s
Southbank and the Globe and TAte Modern or just relax along the river at a pub!

There are no shortage of markets - the question I often ask people is do you want to go to a touristy market or a locals market. Places like Borough Market (food), Portobello Road (bric-a-brac / antiques) and certainly Camden Mkt (punk and incense) have all become very touristy - to get a sense of local London try the East End markets - I particularly like Broadway Market market - see http://wp.me/p2r6no-av for a review on this market. Columbia Road Flower market is also worth visiting - http://www.columbiaroad.info/ as is Brick Lane - http://www.visitbricklane.org/

Columbia Road and Brick Lane can be done on the same day (Sunday morning): they are walking distance of each other. Columbia Road is particularly great – as well as the flower market (with east end Londoners still shouting their wares "3 bunches for a fiver"), the street is also full of interesting arty shops and cafes.

Broadway market is very trendy, open Saturdays only.

If you go to Borough market on the Saturday, make sure you also visit Maltby Street market, held in the railway arches of architectural salvage firm called Lassco. Much less packed and much hipper. http://www.londontown.com/LondonInformation/Shopping/Maltby-Street-Market/ae48d/

As above Borough and Camden are the ones I tend to focus on - that said I am pretty ignorant of the others - I need to get out more.

Thank you everyone for your input. We ended up going to Borough Market on a very cold Saturday morning: it was delightful. We couldn't believe how old the market was, how vibrant and how varied the merchants. The duck sandwich was heaven and we enjoyed an (early) glass of wine at the wine shop. Loads of fun - easily would return.