You might start with some of the volumes in the seven-volume series 'The
English Satirical Print, 1600-1832", published by Chadwyck-Healey in 1986.
These include:
John Brewer: "The Common People and Politics 1750-1790s"
H.T. Dickinson: "Caricatures and the Constitution 1760-1832"
John Miller: "Religion in the Popular Prints 1600-1832"
J.A. Sharpe: "Crime and the Law in English Satirical Prints
1600-1832"
Peter D.G. Thomas: "The American Revolution"
These books are based in large part on "English Cartoons and Satirical Prints
1320-1832 in the British Museum", published in microfilm by the same
publisher in 1978, and reproducing some 17,000 prints listed in the
"Catalogue of Political and Personal Satires" by F. G. Stephens and M. D.
George. (I believe that this is the microfilm collection to which Professor
Stansky referred in his reply). This collection can be difficult to locate
(neither Nortwestern nor the University of Chicago has a copy), but the books
are readily available and well worth investigating. The full microfilm
collection can be found at The Center for Research Libraries, in Hyde Park.
Richard S. Millard