Gregson was born of Irish descent, and grew up in Wavertree, Liverpool, where he was educated at Greenbank Road Primary School and later at St. Francis Xavier's College. He left school at 16, working first for a telephone company, then for Liverpool Corporation, as the city council was then known, before the Second World War. During this time, he became interested in amateur dramatics, joining first his local Catholic church theatre group at St. Anthony’s, Mossley Hill, and later the Liverpool Playgoers' Club.