I may be way off the mark here, but just to throw a heap more confusion into the mix
First marriage of William Henry Kedge (transcribed as Redger)
10 July 1851 St Luke
William Henry Kedge, Full Age, Bachelor, Porter of Hull Street. Father: James Kedge
Eliza Pinson, Full Age, Spinster of Johns Row. Father: William
Wit: Joseph (?) & Louisa Mary Kedge
Unfortunately the page is torn so I cannot see James Kedge's occupation, nor can I find William Henry in Hull Street in 1851.
Looking for the witness, Louisa Mary Kedge, the best I could find was this:
26 Oct 1856, St Andrew, Bethnall Green
Henry Kipps, Full Age, Bachelor, Tobacco Pipe Maker, 36 Sale Street. Father: James Kipps, Tobacco Pipe Maker
Louisa Mary Hedge, Full Age, Spinster, 1 Charles Street. Father: James Hedge, Tobacco Pipe Maker
Wit: James & Eliza Cale
1841 Little Whites Alley, Finsbury. Piece 686, Book 18, Folio 10, Page 15
James Hedge 25 Tobacco Pipe Maker - N
Jane Hedge 25 – Y
Louisa Hedge 5 – N
Jane Hedge – Y
1851 The Cottage, Kingsbury Place HO107/1512/444/5
Jane Hedge Head 38 Pipe (Tobacco) Maker b Northolt, Middx
Louisa Hodge Daur 14 b Tower St, Middx
Jane Hedge Daur 12 b Liberty of the Rolls, Middx
Elizabeth Hall, Aunt, Unm, 78 b Wilts
HO107; Piece: 1512; Folio: 444; Page: 5
5 Jun 1836, St Mary, Newington
Louisa Mary d/o James Collins & Jane Hedge, Weymouth Street, Tobacco Pipe Maker (born 6 May)
7 Jun 1835 St Dunstan in the West - James Collins Hedge m Jane Phillips
William Henry's age in the census is c1830, so a possible baptism?
2 Feb 1830, St Marylebone
William s/o Louisa Sawyers & James Hedge – workhouse (born 6 Jan)
As I said, I could be completely off the mark, but it might be worth obtaining a copy of the 1851 marriage certificate to see what the occupation of William Henry's father was. If it was Tobacco Pipe Maker then possibly his surname was originally Hedge/Sawyers - assuming of course that the John Farnell Kedge in 18
781 is actually John Henry and the two are therefore connected somehow