Is this your Frederick in 1871?
2 Church Lane, Hampstead RG10/191 folio 62 pg 30
Frederick Hall head mar 37 hackney carriage driver b. Oxon, Benson
Sarah wife 40 b. Sussex, Rodmell
Frederick W son 8 b. Surrey, Peckham
Herbert son 3 b. Middx, Hampstead
birth reg for Frederick W dec qtr 1862 Camberwell 1D pg 514 mmn Hutson
If so, you're looking at the wrong Richard & Harriet as Frederick was born in Oxfordshire
1851 census Benson, Oxfordshire
Richard Hall head mar 54 Ag lab b. Berkshire, Radley
Harriot wife 50 b. Radley
John son 27 ag lab b. Benson
Frederick son 17 ag lab b. BensonHenry son 15 ag lab b. Benson
Richard son 10 errand boy b. Benson
William son 8 b. Benson
1841 census Tidmarsh, Ewelme HO107/881/8 folio 22 pg 16
Richard Hall 40 ag lab
Harriet 40
James 15 ag lab
John 13 ag lab
Edward 12 ag lab
Thomas 10 ag lab
Frederick 7Henry 5
Susan 1
Richard 3 months
all born Oxfordshire except Harriet
Birth regs for Susan, Richard & William at Wallingford have mother's maiden name of
HughesMarriage 31 March 1823 in Burnham, Buckinghamshire for Richard Hall & Harriet Hughes
https://www.familysearch.org/ark:/61903/1:1:NNGL-G82Richard Hall of Benson from the BTs, witnesses Stephen Simmonds & James Collins
Harriet was baptised 5 Oct 1800 in Radley, daughter of Thomas & Susannah
https://www.familysearch.org/ark:/61903/1:1:NKKF-96BCan't see an obvious baptism for Richard, but he doesn't help with census entries as 1841 says born in county and 1851 & 1861 say Radley, Berkshire. Also, there's not a huge amount of records for Berkshire & Oxfordshire online from that period. But I'm certain it's not the one Finsbury one.