This stereotype goes back to World War II, when American and English servicemen intermingled. The British were massive consumers of tobacco and refined sugar, with limited access to dental care. At the same time, U.S. dental care was advanced, extensive, and affordably accessible.
Since WWII, the situation has reversed. In the U.K., free/low cost dental care is provided to all, and every child gets prenatal and pediatric health care. U.S. dental care has become extremely costly and isn’t covered by standard medical insurance; attractive, healthy teeth are the privilege of those who can afford them. Many Americans never see a dentist and start to lose teeth in young adulthood.
Yet, the old stereotype still persists and is the subject of much humor.