Christie Brinkley experienced the "worst kind of loneliness" towards the end of her relationship with Billy Joel

Writing in her new memoir 'Uptown Girl', which is being serialised by People magazine, Christie said: "To be clear. I never wanted to end things with Billy. But his drinking was bigger than the both of us.

"In the end, when the relationship isn't functioning the way you want it to be anymore - that's the worst kind of loneliness because you just can't make it work together and that's painful."

Christie famously appeared in the music video for Billy's 1983 hit single 'Uptown Girl' but revealed that the singer wasn't looking at his finest when the pair first met.

The blonde beauty wrote: "He definitely didn't look like a rock star.

"The man was sunburned to a crisp, his face the same colour as cranberries and unctuous with oil, which he'd undoubtedly slathered on to soothe the burn, topped by what I like to call 'the Long Island bubble': a carapace of curly shellacked hair popular in the 1980s in parts of suburban New York."

Christie admits that she found Billy's charms irresistible, particularly when the artist performed on stage.

She recalled: "We laughed like you couldn't believe.

"But he was also sensitive and he did all the old-fashioned things, the flowers, the notes and the poems and the songs. He was going into the recording studio and he was writing all these songs and saying, 'This one's for you.' How could I not fall in love with him?"

Brinkley added: "When I heard him sing on stage. I found myself undeniably attracted to this physically hot and charismatic man."

Christie and Billy - who have daughter Alexa Rae Joel, 39, together - still have a "great" relationship over three decades on from their divorce.

She explained: "He lives mainly in Florida so we don't see him as much as when he lived in Sag Harbor, but when he comes by to see Alexa, he'll come in and say hello."