11.9.1807 dine at Johnson's w. Gooch /  2.2.1820 seek Gooch
The only two Gooch entries in Godwin's diary, and 12 years between them, so they may not have referred to the same person, Possibles:
Robert Gooch (DNB 1784-1830) had graduated MD from Edinburgh in June 1807 and then worked for a time under Astley Cooper in London. He could have also been the 1820 entry.
Rev William Gooch whose General View of the Agriculture of the County of Cambridge was printed for Richard Phillips in 1811 but the preface signed Whatfield parsonage Suffolk 1807. He was born about 1761 son of Henry Gooch, mercer of Gorleston, Suffolk, BA from Caius college Cambridge 1792, died 12.12.1813 at Douglas, Isle of Man (Alum Cantab), his will PCC 7.9.1814 of Templepatrick, co. Antrim
Holdens directory 1811 (court) Charles Gooch esq 32 West-sq, St Geo Southwark / Capt Geo Gooch 28 Brunswick-sq / Henry Gooch, 1 Union-row Camberwell / Thomas Sherlock Gooch esq Clarges-st MP for Suffolk (not at all radical) / Mr John Gooch 13 Queen-st Brompton