The Fab Four to some extent perhaps at that time in that they were already the best known and most successful British Invasion group but the fabs and others would all tell you all the British groups initially were channeling the American roots music including blues, rock and roll and/or soul of teh 1950s. Chuck Berry, Buddy Holly, Muddy Waters, Elvis and all the rest.
It all changed when the Beatles emulated The Beach Boys Pet SOunds and struck out on their own with Sgt. Pepper. The Moodies followed suite in their own way with Days of Future Passed. As did The Kinks, Stones, Hollies, and so many more. Then rock was never quite the same again as its simpler roots.
So it all started in America but took off from there overseas. Where have we heard that story before?