The report says schools have benefited from a stable political leadership and an effective executive director of education, Althea Efunshile. However, there are only modest signs of higher standards in schools.
Over the past seven years the number of failing schools has been reduced. There are currently one secondary and two primaries on the failing list. The secondary has been given a fresh start and re-opened as Teleraph Hill.
The education service is recruiting a chief inspector, but there has been uncertainty about the post for 18 months. The previous chief inspector resigned following a long period of illness.
Inspectors say the lack of a chief has meant the drive to improve standards has been slower and less effective than it might have been.
Lewisham is the third largest London borough and one of the most diverse. In schools, 50 per cent of the pupils is black or from another minority ethnic group.
The re-inspection of the London borough of Haringey, scheduled for June, has been postponed until next year.