22.12.1788 see John Walker.
J Walker was in Godwin's 1796 list near the end of 1788, crossed out, and in 1794 version as John Walker.
Since Godwin saw him after dining at George Robinson's this may well have been Robinson's brother-in-law 'the book-auctioneer of the trade' mentioned in the DNB article on the Robinson family of booksellers. But John Walker was a very common name.
17.7.1795 at Amelia Alderson's, John Walker & Capt Hamilton / 17.7.1805 John Walker at Joseph Johnson's / 27.11.1805 J Walker there, see Walker
11.1.1809 call on Clark (Chamberlain) adv. Walker / 23.9.1809 call on Walker / 17.11.1809 again / 3.12.1811 call on Cobbet; adv. Walker / 18.12.1811 again / 17.6.1812 call on Walker, 44 / 29.11.1817 call on Walker / 1.12.1817 Walker calls
John Walker publisher bookseller 44 Paternoster-row from 1782 to 1828 (bbti) is quite likely especially for 23.9.1809 and 17.11.1809 where Godwin was calling at all the main bookshops. He was brother-in-law to George Robinson 1736-1801 in DNB Robinson family, who was Godwin's chief patron. I've lumped the seven entries above together as there's a 6 year gap in unidentified Walkers before and a 12 year gap after. But the two entries at Cobbett's may have been someone else, likewise the two entries close together in 1817