June was born in Laburnham Road, Redcar, North Yorkshire, England, where her parents operated The Royal Hotel on the sea front near the pier. Prior to that, they managed various hotels and pubs in Redcar and Easington before taking over the Castle Hotel in Bishop Auckland, County Durham in 1956, and subsequently the Royal Hotel in Redcar in 1965.
June's early education took place at White House School in Redcar, where she was bitten by the acting bug after appearing in a school production of 'Romeo and Juliet'. She then took ballet lessons from the age of 11, winning cups and medals, including the Junior Medal at 12 and the Senior Medal the following year.
June joined the prestigious Saddlers Wells Ballet Company in 1946 and performed with Saddlers Wells and Covent Garden. Around 1951, she saw a production of 'Brigadoon' and realized that she would rather work in that type of production.
In 1952, June was part of the chorus in Ivor Novello's 'Gays the Word' when a girl with a speaking part fell ill, and she took over the role to great acclaim. The hairdresser Steiner asked to be introduced to her and used her as a model, resulting in an appearance in an episode of Pathe Pictorial, which led to her being recruited by the Rank Organisation in 1956.
June attended the Rank Organisation's acting prep school, often referred to as 'The Charm School', which had launched the careers of notable actors such as Donald Sinden, Diana Dors, Dirk Bogarde, and Christopher Lee. She made her film debut as a hospital receptionist in 'Doctor at Large', which led to her being picked out by an Italian production company and appearing in 'Souvenir D'Italie' with Vittorio Gassman.
June's big break came when she replaced Anthea Askey in the role of Dickie Henderson's wife in the TV series 'The Dickie Henderson Half Hour', which continued into 'The Dickie Henderson Show', and combined ran for over 100 episodes. She retired from acting in 1966 before the next series, 'A Present For Dickie', but returned in 1970 to appear in the final episode.
After retiring from acting, June returned to Redcar, where she became the owner of The Royal Hotel on the High Street, taking over the licence from her parents in February 1971. She changed her name back to Laverick by deed poll. June eventually gave up the hotel in October 1975 and moved back to London to try and get back into show business.
June was married three times: first to Denny Bettis, an I.C.I. worker, in August 1952, but the marriage didn't last and they divorced in 1956. Her second marriage was to Peter Glover in June 1964, who died suddenly a short while later. In August 1965, she married I.C.I. worker Ian Welton and retired from show business. They had a son, Paul Harrison Welton, in 1967, but separated in 1969 and divorced in 1971.
June's third marriage was to Charles Cooke, a Redcar engineer, in August 1975, but they separated soon afterwards. She then returned to the south, where she became romantically linked with Hughie Green, the quiz master of TV's 'Double Your Money', living in adjoining flats in a block above Baker Street Tube Station in London.
After Hughie Green's death, June returned to the north, settling in South Hetton, a mining village in County Durham, where she died at the age of 66.