As others have said, the nearest Farmer's Market are Dulwich and Hilly Fields.

Dulwich Farmers' Market,
South Gravel,
Dulwich College,
Dulwich Common
? Selection of meat, cheese and vegetables.
? Managed by City & Country Farmers market Ltd
? On 4th Sunday of the month. 9am-1pm.

Hilly Fields

The farmers' market at Hilly Fields is held every 2nd Saturday of the month throughout the year. Hilly Fields has been running since April 2003 and there are about 15 to 20 stalls depending upon the time of year.

Bus: 484, 122
2nd Saturday of the month 10am?4pm

If you just want a street market, then I find that Lewisham High Street or Croydon are the easiest to get to by public transport.

You could try Lewisham's, Southwark's or ViewLondon's websites for details of other nearby markets.