The Billy Ireland archive is located at Ohio State University in Columbus. From their website: ‘The Billy Ireland Cartoon Library & Museum houses the world’s largest collection of materials related to cartoons and comics, including original art, books, magazines, journals, comic books, archival materials, and newspaper comic strip pages and clippings.’
A quick search produced 38 works by Rowlandson, 48 by Gillray (some were pages of his notebook rather than cartoons), 70 by the Cruikshanks). Each image carries information about copyright. Those I looked at stated that although OSU believed the image was in the public domain, users should assess copyright for themselves.