I could give you a list of respected books on British artillery, none of which have any references to such a weapon. The smallest British (weapon) mortar I'm aware of is the 4.5-inch Coehorn.
Ft. Ticonderoga has a "real" wrought iron mortar with smaller bore, but the provenance is uncertain as I recall. Just because it is in the F.T. museum means nothing; they got donations from a lot of different sources and like many museums, didn't challenge the stories, if any, that came with the junk.
George Neumann is highly respected within our Company of Military Historians, and I've had the pleasure of being able to call him a friend for decades, but even a great man can make mistakes.