Sources

Notes

Date of death comes from VIAF, though unsubstantiated.
Found to be publishing 1830s and 1840s, maybe in 1820s.
Place of work/residence? given as Cloisters, Temple, which shows in directories in 1840s-1851, and a William Hayes 1856 in 4 New square Lincoln's inn (?? same or different person)
Was of Middle Temple, and MT records show admitted 1808, and called to Bar 1818. Son of William Hayes, Taplow, Buckinghamshire. => born prior 1792
No record showing for Oxford or Cambridge
Nothing showing in ODNB.
FreeBMD deaths for 1871 where born before 1792

Deaths Mar 1871
Hayes William 85 Croydon 2a 130
Deaths Jun 1871
Hayes William 80 Spalding 7a 209

Reasonably common name and hard to pick out in census, nothing evident to identify more accurately
reference to daughter http://www.forgottenbooks.com/readbook_text/Debretts_House_of_Commons_1000691037/125

Births, Deaths, Marriages and Obituaries. The Morning Post (London, England), Monday, February 06, 1871; pg. 8; Issue 30316.

DEATHS
…
Hayes.—On the 31st ult, at The Priory, Norwood, Surrey, William Hayes, Esq., senior conveyancing counsel of the Court of Chancery.