Sorry that's not correct about the K &ESR it was never part of the Southern Railway. It was one of the small independent railways that was not part of the grouping. It only ceased to be independent upon nationalisation in 1948. The Headcorn to Tenterden section was closed and lifted in 1955 with the passenger service removed from the rest of the line. Tenterden to Robertsbridge closed to freight in 1961 so the whole closure predated Beeching.
Fair point. Should have been clearer, so will lift this from Wiki:
"By 1924, the section from Tenterden to Headcorn was operating at a loss. Correspondence with the Southern Railway in 1930 led to Sir Herbert Walker stating that there was no chance of the line making a profit, and that even if passenger services were withdrawn, it was doubtful whether the receipts from freight traffic would cover operating expenses. The Southern Railway were liable to make up any operating losses, as the successor to the South Eastern and Chatham Railway under the terms of the Act of Parliament for the construction of that section of line."
The fact is the line had been identified as unviable before WW2 and had that not happened the line would either have gone bust or been subsumed by the Southern and almost certainly closed.