The star was a teenager when war broke out, and speaking to Kirsty Young, she admits to falling in love with a man, called Ralph Latimer, who later worked as a secret agent.
She explains: “He had escaped from Belgium, Father felt sorry for him because he was on his own in digs and he said to Mother, ‘Can he come and stay with us?’ And he became like a brother. And he also had a very good voice.
“And we all used to stand around the piano and he’d sing and we’d sing. And I was very much in love with him. And he told his mother he was going to marry me when I was 16.
“In that time, they decided they would use him in a better fashion, and he was dropped into Belgium to join The Underground. He became a spy.”
Sadly, it wasn’t meant to be, as June explained that he later returned to England with a woman he was about to marry.
“That was very sad,” she concludes. “I suppose it did break my heart. I was stunned when I realised what had happened.
“We were always writing to each other and the letters just stopped and I didn’t know what happened. And I did actually write and say I’ll be coming up to London. And I’ll be there all day, which I was.
“And apparently his mother came to meet me but I’d just gone to a restaurant. We just missed each other.”
June is the latest in a long line of stars to decide on their Desert Island Discs, and the Radio 4 show recently celebrated its 75th anniversary, with David Beckham taking part.