Carly Simon: How Mick Jagger's Wife Accused Her of Cheating on James Taylor the Night Before Their Wedding

"If Mick could have his way, it would be Romeo and Juliet tragic. We couldn't have each other," Simon writes in her new memoir.

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Carly Simon is opening up about her relationship with Mick Jagger in her new memoir Boys in the Trees, out today.

The three-time Grammy-winner – who was engaged to James Taylor at the time – recalls the feelings of "raw electricity" between her and the Rolling Stones frontman during recording sessions for her soon-to-be smash hit "You're So Vain" – a mutual attraction so hot that "having sex would have actually cooled things off."

"If Mick could have his way, it would be Romeo and Juliet tragic. We couldn't have each other," Simon, 70, writes in her book. She doesn't say exactly how far the dalliance went, but she reveals that the night before she and James married, he got a call from Mick's new wife Bianca.

"James and I were in bed, getting ready for the big day, when the phone rang and James answered. It was Bianca Jagger," Simon writes.

"She told James that he shouldn't marry me because her husband and I were having an affair. She muttered some things I couldn't believe she was saying. Then James said, 'I'm sure that's not true. Carly has told me about it and it s not what you think. I trust my wife-to-be. I trust Carly.' "

Simon and Taylor married in 1972, but she continued to receive roses and sweet sentiments from Jagger occasionally.

In the end, Simon's love for Taylor eclipsed any of her other romances. Fans had long speculated about the subject of "You're So Vain," considering potential candidates including Taylor, Jagger, David Bowie, Warren Beatty, Kris Kristofferson and Cat Stevens.

Simon finally confirms in her book that the second verse of her famous song indeed refers to Warren Beatty.

Now, more than 30 years after their turbulent split, Simon says her love for Taylor endures – even if it's not reciprocated.

"I still want to heal him, I still want to make him all right," Simon told PEOPLE, while confirming that the two do not speak. "And I love him so much."