853 blog covers South East London, particularly Greenwich.
e-Shooters Hill blog has lots of info about events and things happening near the Shooter’s Hill end of Blackheath.
The Blackheath Bugle covers Blackheath with a particular focus on the village.
The Charlton Champion covers Charlton-related matters.
The Westcombe Society has a website / blog which covers that area of Blackheath.