Just outside the perimeter of current Gatwick Airport, nestled within a modern business park, sits the original terminal from the old Gatwick Airport. It’s called the Beehive and was the world’s first purpose-built airport terminal to provide covered access to aircraft.

It was also the first aircraft terminal to link directly to a railway station. This was via a tunnel just over 100 metres long. You can see that station in this Britain From Above photo. The new Gatwick Airport Station is further north than this one (to the left of this photo).

Something still visible are the rails where the six telescopic corridors ran. They extended from the terminal to the aircraft steps. You can also see in the centre of the building the original air traffic control tower.

The Beehive was built in 1936 by and used until the 1950s when it became obsolete due to airport expansion. Today, the building is offices. As always, the amazing Britain From Above website has helped fill in the research gaps.

https://britainfromabove.org.uk/en 

Aha, this is the photo I was looking for. The Beehive taken from the original station. There's more great photos of the station (including one showing a Beehive telescopic corridor) on this excellent website.
http://www.british-caledonian.com/Gatwick_Airport_-_The_History_P2.html