During the war, the bombings of 1940 forced the Government to discuss the need for deep-level air-raid shelters and by the end of October it was decided a system of deep shelters linked to existing tube stations was the best option. London Transport was consulted about the sites and it was agreed they would build them at the public expense with the understanding that they were to have the option of taking them over for railway use after the war.

Each shelter consists of a pair of parallel tunnels 16 feet 6 inches (5.03 m) in diameter and 1,200 feet (370 m) long. Each tunnel is subdivided into two decks, and each shelter was designed to hold up to 8,000 people. 10 Tunnels were planned, but only 8 were built. 

These were at:
Belsize Park
Camden Town
Chancery Lane
Clapham Common
Clapham North
Clapham South - This site is available to visit. For tickets and more information click here
Goodge Street
Stockwell

More in depth information can be found here:

https://www.ltmuseum.co.uk/collections/stories/war/deep-level-shelters
https://londonist.com/london/secret/where-to-see-london-s-secret-deep-level-shelters
https://www.subbrit.org.uk/features/deep-level-shelters-in-london/

The London Transport Museum have made 3 videos for Clapham South and these can be seen:
https://youtu.be/Cj4zZil_eNc 
https://youtu.be/lYbZGkl0xqY
https://youtu.be/iCxd-mBXc6I?si=FLQGOe8z2U1O14JZ