The 'Don't Stop the Music' singer may now be married to the model - with whom he has children Lyra, two, and Margot, 10-months - but when they first met he didn't try and chat her up because he was sure she was out of his league.
Speaking on ITV's 'The Jonathan Ross Show', Jamie said: ''When I met her for the first time I didn't think there was even a remote chance in hell, so I played it really cool which actually worked to my advantage.''
Musician Jamie, 34, is noticeably shorter than his wife, and he admits many people mistake him for being much younger than he actually is.
Telling an anecdote, he explained: ''I tried to buy Sophie a bottle of wine and I had my kids and I was wearing a suit.
''I looked about as grown up as I could be and this 18 year old kid was like, 'No, sorry man, you need ID'. He did not sell me the bottle of wine.''
Jamie has previously said fatherhood has delighted him and changed his perspective enormously.
He said: ''Getting married and becoming a father makes me see the world a lot more intensely; a lot more of the happiness but also the sadness ... When you have kids you have to put your flag in the ground and decide how you want to live your life and the example you want to set.''
The novel's author saw a cut of the film and loved each of the changes the movie's director had made.