When I crossed the railway, I could make out what looked to be a platform. Upon investigating I discovered that it is the long lost Woodcroft Halt. Wikipedia describes it thus:
During World War II, in 1940 the Admiralty requisitioned Ditcham Park, a nearby country house for use as a convalescent home for sailors (the house is now a private school). The halt was built to serve Ditcham Park, principally for trains from the extensive naval facilities in Portsmouth about 20 km (12 mi) away. Woodcroft Halt, which was also known as Ditcham Park Halt, opened on 4 October 1943, and closed on 1 October 1945.
Because of its naval nature, it was featured on few maps, but some maps did mark it by a little tab without a name.
It was closed in 1945 and subsequently demolished. Today, only a footbridge remains.