The Hawkhurst Branch in 1958

Built on the cheap and opened as late as 1892, the Hawkhurst Branch ran through the orchard and hop country of Kent.

Plans for extensions to Tenterden, Appledore or Dungeness came to nothing and the line was thoroughly uneconomic when it closed in 1961.

Wikipedia records the intriguing detail that:

Elisabeth Beresford, who was subsequently well known as the creator of The Wombles, wrote a children's book Danger on the "Old Pull 'n Push" based on the Hawkhurst branch. 

Subsequently this was televised by Rediffusion for ITV in two six-part series The Old Pull 'n Push and Return of the old Pull 'n Push, shown in 1960-61. These were filmed on the Hawkhurst Line shortly before it closed.