I am interested in finding both his parents details and his wife's maiden name.
Any indicators would be most appreciated.
I can look for you but the best solution would be to get William Nelson Cooks marriage Certificate. From your information I have managed to find a baptismal record for William (Not a hard copy) DOB is a ??1829 but date of Baptism was 3/7/31. You can find him in the 1861 census with DOB of 1829 with Mary Ann DOB 1833 Ireland so am guessing this reference to a marriage certificate is correct Dec 1855 1c 828
Children registered as surname Cook, mothers maiden name Leader:
William Nelson Cook, Reg St George in The East, 1856 (death registered same year)
James Nelson Cook, as above, same reference, also died 1856
Mary Ann Cook, Reg St George in the East, 1858
Elizabeth Jane Cook, as above, same reference
Catherine Cook, Reg Stepney 1863
William Nelson Cook, baptised at St Peter & St Paul Swanscombe 3 Jul 1833 (born 1829), son of James and Ann.