There was a passenger service via East Putney, but this has been mentioned in another posting. I understand that there has never been a direct connection between the West London Line and the main south-western lines at Clapham Junction, so traffic would need to go via East Putney to join the main line at Wimbledon. My dad tells me that he was on a troop-train during the last war from West Runton in Norfolk to Aldershot that went via Stratford, Willesden Junction, Clapham Junction, East Putney, Wimbledon and then on through Woking. Despite commuting for many years up to Waterloo, this was the only time he'd ever been via East Putney.
The abutments for the up bridge East Putney are still in place, and I read somewhere that the bridge could be reinstated should traffic ever require this.