There are some Radford entries on FreeREG in the right time but not who your looking for
(I even tried William Bowles in case his Parents married after his Birth)
I see in 1841 William is a Shoemaker and 1851 a Superintendant of Police
I found his Daug Rebeccas Baptism 05 Jan 1834 and noticed other Raynor Baptisms around the same time;
EG;
JOSEPH LAMBERT Raynor 24 May 1830 to GEORGE/REBECCA, Cordwainer
REBECCA Raynor 18 Apr 1826 to JOHN/MARY, Cordwainer
3 Shoemakers pricked up my interest, Brothers?
I looked for Joseph Lambert Raynor in 1851 and came up with this;
1851 Census
Nottingham St Mary
HO107/2132/557/4
Joseph Raynor, 77, Head, Widr, Constable**, born East Markham, Nottinghamshire
Rebecca Raynor, 44, Daug, Unm, Tambourer of Lace, born Sheffield, Yorkshire
Mary Ann Raynor, 40, Daug, Unm, Tambourer of Lace, born Sheffield
Elizabeth Raynor, 37, Daug, Unm, Tambourer of Lace, born Sheffield
JOSEPH Raynor, 20, Grandson, Warehouseman, born Nottinghamshire
John Raynor, 6, Grandson, Scholar, born Nottinghamshire
Occps seem to much of a coincidence to me.
1841 Joseph is s Shoemaker;
St Mary, Notts
HO107/869/1/St Mary
Joseph Rayner, 68
Ann Rayner, 66
Rebecca Rayner, 35
Mary Rayner, 28
Elizabeth Rayner, 26
JOSEPH Rayner, 11
Only Joseph age 11 is down as born in County
All the Girls are Lace workers.
Maybe right off here but I have a niggling feeling Joseph is a possibility for Williams Father.