The William from Great Bedwyn has his supporters.
Ah, that's your Hiscock!
I keep coming with the name of Hiscock.
Baptism at Great Bedwyn, 2 Dec 1838
William
illegitimate son of Ann Hiscock, Widow
Abode Marten
Born 29 October 1838
Marriage at Great Bedwyn, 30 Dec 1843
John Richardson, Bachelor, Laborer, father James Richardson deceased, Laborer
+
Ann Hiscock, widow of James who left 2 sons + 1 daur (wow!), father John
Bushell, Laborer
Both full age, residence Marten
And there is the Bushell maiden name!
RICHARDSON, WILLIAM BUSHEL
GRO Reference: 1838 D Quarter in HUNGERFORD UNION Volume 06 Page 173
1841 in Great Bedwyn
https://www.familysearch.org/ark:/61903/1:1:M73P-2CTThomas, Elizabeth and Charles Richardson in the same household!
So the William Richardson Dec 1838 birth reg was to John and Ann (but not married)
And the Charles Richardson June 1839 birth reg was to the Thomas and Elizabeth also in Great Bedwyn
Incredible!