Your father William George Bradshaw's birth is registered 1944 Manchester (8d/488, q June with mother's surname HENSHAW. Unfortuntely, marriage registrations of Bradshaw/Henshaw between 1930 & 1950 in England & Wales are silent. I would suggest you purchase the birth certificate William George, from General Registry Office, quoting the above details; that certificate will name both parents.
Your parent's marriage is registered 1967 Manchester (10e/365 q March). A Joan Middleton's birth is registered q September 1940 (Darlington 10a/6), with mother's surname FAIRLESS. All other Joan Middleton's have a middle name.