You might like to consider the possibility that Henry is actually Henry Tudor Hall.
A Henry Tudor Hall s/o William and Lydia was born at Long Ashton, Somerset (about 4 miles from Bristol) in 1802 - shown on familysearch.
One son (another Henry Tudor) of Henry Tudor Hall and Elizabeth was baptized at St John the Evangelist, Lambeth in 1832. Henry is a blacksmith.
Marriages of children of Henry Tudor Hall (smith)
William Hall m Mary Ann Broom 1841 Lambeth St John the Evangelist (one witness is a James Green)
Elizabeth Tudor Hall m David Thomas Wardle 1857 St Mary, Lambeth (Elizabeth's father is deceased)
George Tudor Hall m Sarah Crockett 1858 St George the Martyr
There is also a Maria Hall d/o Henry Hall (smith) deceased who married Henry James Pitcher at St Mary, Lambeth 1854
and a widower Matthew Hall marrying Hannah Sheen at Walworth St John in 1877. Matthew's father is simply Henry Hall (deceased), but Matthew is himself a blacksmith.
There is a family of Henry and Elizabeth Hall in Lambeth in 1841 which includes children with all the above names, as well as a 15 year old Eliza. Henry is a smith, but he and Elizabeth are aged 45. They all are down as born in county.
[Census ref: HO107/ Piece: 1061/ Book: 6/Folio: 5/ Page: 4]
So not conclusive, although I have found the born in county/not born in county 1841 recording is not always reliable.
William Hall, smith (he is a smith in 1841) shows up with his wife Mary Ann in 1851 in Lambeth - his birthplace is shown as Liverpool.