AFAIK 'Greenwich' covers the borough of Greenwich, so not strictly Greenwich town centre.
Greenwich and Blackheath sort of merge into each other via Greenwich Park and Blackheath Common, don't they? It's a difficult one, as much of Blackheath is in the borough of Lewisham. Have you looked on the Lewisham local site?
When I add local listings to the Greenwich site, I have added some that are 'over the border' and fall into Lewisham or Bexley. These still show up under Greenwich 'local listings' as the listings do not take into account borough boundaries.
Perhaps we need to have some links to the Lewisham and Bexley sites on the Greenwich site home page?