Cobbett is almost entirely unknown in the United States on a pop-cultural level. To the degree even those with an education or avocation in history have ever heard his name it's entirely in relation to his role in the mis-placement of the remains of Thomas Paine. Sometimes works on the history of pamphlet literature in the so-called Federal period of the Early Republic (1789-1820) will have a brief mention of Cobbett's name, as he was a prominent pamphleteer of that era.

Overall, William Cobbett is very obscure in the United States. His political writing was largely on subjects that were not of lasting political impact (from a U.S. perspective), unlike his contemporary William Wilberforce, whom is very well-remembered in the United States for his anti-slavery activism and writings.

Does that help? How well is Cobbett known in the UK?