Primarily because of the less expensive costs, we, here in the U.S., see a lot of foreign nationals, especially Brits, coming to the U.S. for flight training on Student Visas. There are numerous large and small flight schools, many accredited and associated with Universities. Two of the largest are Embry/Riddle with two locations; one in Prescott, AZ and the other main one in Daytona Beach in Florida. Another that trains pilots for airlines worldwide is the University of North Dakota in Grand Forks, ND. The significant advantage for training at facilities such as these is the granting of a graduate or associate degree along with the requisite pilot's certificates (their called certificates in the U.S. vs. licenses in many other countries) as well as their close relationship with many client airlines... Best of luck!