according to SCOTT WALKER: A DEEP SHADE OF BLUE by Mike Watkinson & Pete Anderson, Scott first proposed to Irene Dunphy in the mid-sixties who turned him down because she thought he was "so unstable at the time".
He did marry Mette Teglbjaerg, a Danish fan, in 1974 and they have a daughter Lee who is now 34. they divorced within two or three years of marrying, partly due to Scott's constant attentions from fans.
as the book was written in the early 90s and the copy i have has an afterword from 1994, it is not widely known if Scott is married now (though googling recent news artciles relating to his new album and Imagine programme may possibly help).
dont actually think this has helped but wanted to add my bit.