The club next to intersection of Beckenham Hill and Bromley road (with their entrance in the Homebase car park drive) is called Catford Wanderers.

I used to be a member when I lived closer to the club, and can really recommend it. They have both hard courts and grass courts, and a great clubhouse. They also have badminton, football and cricket. A very friendly club.

http://www.catfordwanderers.co.uk/tennis/index.htm