Terence Henry Stamp was born in Bow, London on 22nd July 1938. His parents, Thomas and Ethel Stamp, had five children in total, of which Terence was the eldest. One of his brothers, Chris Stamp, later became a rock ’n’ roll impresario managing The Who and The Crazy World of Arthur Brown. His other brothers are Richard and John, and he has one sister.

As an infant Stamp’s father Tom was often away for long periods with his job in the Merchant Navy, so young Terence was primarily raised by his mother, aunts, and grandmother Kate. Tom was a stoker (i.e shovelled coal into the fire under the ship's boiler). This is was a hard job, physically very demanding. Later, during Terence's youth, Tom became a Thames tug-boat captain and was therefore home each night. Tug boats are used to guide ships through narrow waters, as well as move vessels that cannot move themselves.

Later during his childhood the family home moved to nearby Plaistow (pronounced "plah-stoh"), an urban area in East London.

The young Terence grew up wanting to be the film actor Gary Cooper (aka "Coop") after his mother had taken him to see his first film, the classic French Foreign Legion epic Beau Geste (starring Gary Cooper. 1939) when a small boy.

Stamp was dissuaded from being an actor by his father who more or less said “People like us don’t do things like that”. On leaving school Stamp worked in a variety of London advertising agencies, and in a relatively short space of time had worked his way up to a respectable wage. However, deep down he was still drawn to the world of acting.