Beckley was born in Southampton, Hampshire, England. He was a child out of wedlock and never met his father. His mother, Beatrice Mitchell, was a stewardess who worked on ocean liners such as the RMS Mauretania and the RMS Aquitania. Due to work commitments she was often away and Beckley was brought up mainly by another lady he referred to as his aunt.  When he was five years old Beckley and his mother moved to Portsmouth and when World War II broke out he was sent to Winchester where he attended boarding school at Winton House. As a school boy he enjoyed reading, English and painting and it was in Winchester where he first became interested in acting. While his mother wanted him to do “something nice and safe”, i.e. working in the civil service, Beckley felt he had discovered that acting was what was going to make him happy when he saw a performance of Emlyn Williams’ “The Corn is Green” by the Portsmouth local repertory company the Court Players.  Beckley left school at the age of 16 in pursuit of his acting career. He worked as a stage sweeper and tea maker for two or three months before moving to London. As he could not get work in the theatre he did odd jobs as a waiter and in an ice cream factory while spending his spare time watching actors like Laurence Olivier, Ralph Richardson and Alec Guinness and the Old Vic productions at the New Theatre.  Shortly before turning 18, he joined the Royal Navy. Beckley spent two years as a seaman aboard the destroyer HMS Scorpion where he found the time to prepare for admission to the Royal Academy of Dramatic Art (RADA). He joined RADA on an ex-Navy grant and during his two-year training befriended people such as actress Sheila Hancock and playwright Charles Laurence.

After graduating from RADA, Beckley started working for various provincial repertory companies, eventually settling with a company near London (Bromley Repertory[6]) which opened up opportunities for television work. After guest roles in popular TV series such as Sergeant Cork, The Saint, Z-Cars and the then revolutionary comedy programme Dig This Rhubarb Beckley made his film debut in 1965 as Ned Poins in Orson Welles’ Chimes at Midnight.  Beckley appeared in a number of films for director Peter Collinson: The Penthouse (1967); The Long Day’s Dying (1968); and most memorably as Camp Freddie in The Italian Job (1969). His only starring role was as the psychotic Kenny Wemys in The Fiend (1972), and he made his last film appearance in 1979 playing another psychopath in When a Stranger Calls. Other films include The Lost Continent (1968), Get Carter (1971), Assault (1971), Sitting Target (1972), Gold (1974), and Revenge of the Pink Panther (1978).  On television he guested on shows such as Manhunt, Callan, Jason King, Special Branch, and perhaps most notably as the villainous Harrison Chase in the popular six-part Doctor Who serial The Seeds of Doom.  He also remained active in the theatre, appearing in the West End in Tennessee Williams’ Small Craft Warnings with Elaine Stritch and in Snap with Maggie Smith.

Beckley died shortly after principal photography was completed for When a Stranger Calls. Just before his death he had been signed for further work in the U.S. He was supposed to costar with Elizabeth Montgomery in a television movie called My Fat Friend and appear in a film (American Dreamer). He was also to appear in the NBC miniseries Beulah Land alongside Lesley Ann Warren, Don Johnson and others.  The cause of his death was given as cancer (brain tumour) but appeared “mysterious”. According to his friend Sheila Hancock it could have been AIDS, a disease then almost unknown. Beckley died at the Medical Center of the University of California at Los Angeles and is buried at the Hollywood Forever Cemetery.