Harris was born in Somerset; her family moved from Midsomer Norton to Bournemouth when she was seven. She won a talent contest at the age of three. However, it was her penchant for figure skating which led to her performing career, she began skating at the neighbourhood rink, eventually becoming a regular at the Queens Ice Rink in London. Seen by a talent scout shortly before her sixteenth birthday, she was offered a chance to skate in Paris or to travel to Las Vegas where she would be a dancer in a chorus line. She accepted the latter, danced at the El Rancho Hotel in Las Vegas. "We did three shows a night and on the 12th night, we had the night off", she said years later.
Since 1961 she has made numerous television appearances, mostly as a performer, occasionally as an actress, and her few film roles included a cameo as a casino singer in Death Is a Woman (1966) and co-starring roles in the comedy films Follow That Camel (1967) and Carry On Doctor (1968). Harris gained her role in the latter film while working in a revue Way Out in Piccadilly with Frankie Howerd. Backstage, he introduced her to the producer and director of the series resulting in the decision to cast Harris as well as Howerd. In December 1970, Thames Television debuted the children's television series Jumbleland which she co-produced and in which she starred as Witch Witt Witty.
In 1966, her debut album was released by CBS Records: Somebody's in My Orchard. Her chart breakthrough came in the summer of 1967 with the single Just Loving You, a Tom Springfield composition which singer Dusty Springfield had suggested that Tom (her brother) give to Harris after Dusty and Harris had performed on the same episode of Top of the Pops.