Arch 3.7.1800 at Colles's (in Ireland) / 17.12.1801 Arch's at Lamb's / 20.5.1805 Arch at Lamb's / 26.9.1809 call on Arch / 16.11.1809 again / 17.6.1812 again / 18.6.1812 again
The only examples of the name Arch I found in Ireland were John Arch born 1748 Dublin and Nicholas Arch married 1773 Dublin. As with Tobin, Hume, Higgins, Ridgway and Johnson I reckon the GD website coding of those names in Ireland to Godwin's friends of those names in England is unconvincing, but If Colles was the bookseller Isaac Colles (which is just one possibility, see Colles) then perhaps the Arch in Ireland was one of the booksellers John and Arthur Arch who were probably all of the later entries in London. They published Blank Verse by Charles Lamb and Charles Lloyd in 1798 and were Quakers, in business 1792-1938 according to Maxted, at 61 Cornhill in Holdens 1811, will PCC 1815 John Arch publisher of London Price Current, Bethnal Green, PCC 1839 Arthur Portsmouth Arch gent of Winterslow Place North Brixton, PCC 1853 John Arch bookseller of same address