A birth for an Alan C. Whiteman, mother's maiden name Whiteman, was registered in the September quarter 1945 in Coventry, Warwickshire. If this looks likely it might be worth getting the certificate but if the father had disappeared it is quite possible the father's name is not given. Do remember there were something like 2,000,000 Americans of various shapes, sizes and backgrounds milling around (mostly southern) England at that time and girls getting pregnant and the man "being shipped out and never heard from again" was a not uncommon event. You might do better to start from the other end and try getting American records as you do have his name and the date when he was in England. You say the he was a "soldier in the Navy" which is a little odd - if he was in the Navy he would have been a sailor and you would need to trace naval records, not army. I do wish you luck but the name is not very uncommon and if there were two (or more) William Curtis' in the US Navy in England at that time it might be impossible to know which was which. Hope this helps a bit.