The star wed musician Kemp in 1988 and they had a son, Finlay, together in 1990 - but their union was rocked when Frost met Law on the set of 1994 movie Shopping.
The actress admits she felt a strong "force of love" for the Alfie star, but "crushed" the feelings to continue her "idyllic home life" with Kemp.
In her upcoming autobiography Crazy Days, Frost reveals, "I knew that by even entertaining thoughts of Jude, I was jeopardising an idyllic home life, the most secure relationship I'd ever had. I crushed my unwelcome ideas about Jude, but it wasn't easy.
"The force of the love I felt for Jude and his intense ambition made me feel out of control."
Frost divorced Kemp in 1995 and wed Law two years later (97). They went on to have three children before divorcing in 2003.