Here is a stone train negotiating the connection, have just passed through Wimbledon station on the Sutton reversible and crossing to the SWML down slow.
6O15 1201 Willedsen to Chessington (T Th F O) arr Chessington 1354
6M17 1942 Chessington to Willesden (T Th F O)
The Chessington stone terminal opened in 2021. Until the 1980s there used to be a coal concentration depot there, and trains serving that took the same route.
Here is a Class 73 on such a train at one of the stations on the branch (probably Chessington South but the stations on the branch all look very alike). The presence of a 508 dates the picture to the late 70s/early 80s.