16.8.1796 Palmer at Hewlett's / 1.7.1800 Palmer (Wrexham) on Holyhead coach & on wherry to Dublin / 22.12.1804 call on Palmer / 31.12.1804 again / 8.1.1805 Palmer calls / 2.6.1805 Palmer adv at Philips / 30.9.1809 write to Palmer / 7.2.1811 call on Palmer / 4.11.1813 call on Palmer with Bagley / 11.11.1815 Palmer at Knowles's / 13.3.1820 H Palmer at Telford's, calls / 23.3.1820 H Palmer dines / 17.4.1820 call on H Palmer / 25.4.1820 again / 26.4.1820 H Palmer au soir / 28.4.1820 call on H Palmer / 1.5.1820 seek H Palmer / 2.5.1820 call on Palmer / 3.5.1820 call on Palmer adv Telford & sir H Parnel / 19.10.1821 H Palmer calls / 9.11.1821 again / 25.11.1821 H Palmer dines / 9.5.1823 meet H Palmer / 28.5.1823 again / 23.10.1825 Palmer at Rowbotham's / 24.11.1834 call on H Palmer
All the above entries after 1820 were very likely Henry Robinson Palmer DNB 1795-1844 who worked as an assistant to Thomas Telford DNB 1757-1834. Sir H Parnel who called at Palmer's while Godwin was there in 1820 was very likely Henry Brooke Parnell DNB1776-1820 who succeeded to a baronetcy in 1816. Only the 1825 entry which had no initial H could easily have been someone else, as Palmer was a common name. The first entry in 1796 at Hewlett's could have been Samuel Palmer DNB 1741-1813 who was Independent minister at Hackney not far from Hewlett's school at Shacklewell. The Palmer of 1800 may have boarded Godwin's coach at Wrexham and was possibly Sir John Roger Palmer 2nd bart d.1819 of co Mayo Ireland or his brother William Henry Palmer 3rd bart d.1840 whose son the 5th bart lived at Cefn Park, Wrexham. The next two entries were calls in the same string of calls as Luntley (qv) and mrs Hill (see Hill, Primrose St?) so may have had a connection with Primrose St or else been located on that side of town (Bishopsgate/Shoreditch) and the call on Godwin shortly after was probably the same person. The next entry was six months later at  Richard Phillips DNB 1767-1840 the publisher, and the next four were each two years or more apart, so they could even have all been different Palmers. Phillips' visitors were mostly authors, Alicia Tindal Palmer DNB 1763-1822 published her first novel in 1809 / Charlotte Palmer DNB 1762-1834 published her last in 1797 and thereafter ran schools and was imprisoned for debt in 1805 / Shirley Palmer DNB 1786-1852 published a poem The Swiss Exile at Lichfield in 1804 then came to London to complete his studies as a surgeon / Samuel Palmer DNB 1741-1813 mentioned above had his Letters to Dissenting Ministers in 1806 published by Longman & Rees / William Jocelyn Gresham Palmer published his Discourse on the Real Principles of the Constitution in 1809 / John Palmer junior actor (1776-1809 Highfill, Burnim & Langhans) had novels published in 1796, 1803, 1806 and 1811 but none were published by Phillips.
Other Palmers in the DNB worth considering were John Palmer DNB 1742-1818 theatre proprietor, postal reformer and Whig MP for Bath 1801 to 1808, his son Charles Palmer DNB 1777-1851 who succeeded his father as MP for Bath and was a radical reformer / Joseph Palmer DNB 1756-1815 writer / George Palmer DNB 1772-1852 merchant and his brother Horsley Palmer DNB 1779-1858