Yes, absolutely. Of course the migration from Britain to America was far, far greater than movement vice versa (around 2 million British people moved to the USA in the 1800s), and many Americans moving to Britain would have been naturalised citizens returning home. But there were American-Americans who made Britain their home, and many Americans, particularly those of the upper classes, had business and familial links to Britain, and were often educated there (this is where the prestigious "trans-atlantic" accent, the speech pattern adopted my many early cinema actors, emerged from). Business interests and the emergence of multinational companies would also have necessitated Americans moving to Britain (Harry Gordon Selfridge, the founder of the London department store Selfridges was one such American businessman who moved to Britain), and the Anglophilia of the American intellectual elite would also have fuelled relocation (the writer Henry James eventually moved to Britain and spent most of his life and career there). There were quite a few African-Americans who also relocated to Britain, alongside American abolitionists who spent time there, given Britain's early adoption of an abolitionist stance. Some of these Americans were very notable indeed, but the American in 19th century Britain who first springs to my mind is Lady Randolph Churchill (born Jeanette Jerome, a native of Brooklyn), who was the mother of Winston Churchill, and I'm sure there are plenty more less famous examples. This article also outlines the experiences of Americans in Victorian London, and you might find it an interesting read!

Edit - I dug up some further reading you might want to check out:
Alison Lockwood - Passionate Pilgrims: The American Traveler in Great Britain, 1800-1914
Robert E. Spiller - The American in England during the First Half Century of Independence
R. B. Mowat - Americans in Britain
A fascinating post on African-Americans in mid-Victorian Britain