Baptisms not checked of James Box and Barbara, but on Anc and I think it mentioned he was a Weaver, possibly why I ruled out the 1780 James Box, Will.
St Brides, Fleet Street, London, England, 1st August
1819 James Corney married Jane Box, Spinster
In the Presence of:-
Daniel OKeefe
JAMES SMITH27th May 1764 (Banns also online too)
St Bride, Fleet Street, City of London
"
Box & Smith" [margin]
James
Box Batch'r and Barbara
Smith, Spins'r both of this Parish were Married in this church by Banns
In the Presence of Jane Davis ; Edward James
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General Information on St BrideThis page on Family Search has a boundary of St Bride and surrounding Parishes apparently c.1589, bit too early.
https://www.familysearch.org/en/wiki/St_Bride_Fleet_Street,_London_GenealogyIt mentions Farringdon without.
"
St Bride Fleet Street belonged to Farringdon Ward Without and Castle Baynard Ward.
Also known as St Bridget Parish."
Description changed in 1848.
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Back to 1819 - 1820 on Anc
All London, England, Land Tax Records, 1692-1932From a general James Smith search, one return was:-
James Smith
1820
Farringdon Without, City of London
Image of p.1 says this Land Tax book is:-
London, An Assessment made upon the several Inhabitants and Premises in the Precinct of St Andrew in the Ward of Farringdon Without.James Smith £1. [on page 5]
I didn't check for any other James Smith, there are others for 1820 in other books, indexed by Anc under Farringdon Without (bit misleading), but another James Smith, 1820 was in different book title?
Seems the Ward covered more than one Parish?