Well I've never heard of it(You really do learn something new everyday), its around 4 miles from Blackheath
Founded in 1903 and now boasting an 18 hole course running across the valleys, the charming Shooters Hill Golf Club has a fascinating history. 
Shooters Hill Golf Club - Clubhouse
Initially commandeered as an anti aircraft battery in 1940, its use towards the latter part of the war changed to a prisoner of war camp and HQ for the Home Guard.
Nowadays, with 100 acres of land all owned and maintained by the members, plus 10 handsome tennis courts alongside, it attracts players from both the local area and farther a field.