Sometimes, the US and the UK don’t get on particularly well (see, for example: American Revolutionary War, also known as the Battle of the Upstart Colonists in British textbooks).
“POOR OLD ENGLAND endeavoring to reclaim his wicked AMERICAN CHILDREN and therefore is England maimed & forc’d to go with a Staff. shakespeare,” April 1777.
“John Bull Making a new batch of ships to send to the lake,” William Charles, c 1814
“What? You young Yankee-noodle, strike your own father!” 1846
“Ultimatum on the Oregon question,” 1846.
But they’ve become thick as thieves (in most of the meanings of the word) despite (or because?) of the miles between them:
“The laying of the cable—John and Jonathan joining hands,” c. 1858.
c. 1898 sheet music
Another 1898 poster.
John Bull and Uncle Sam, c. 1900
“The Fable of John Bull and Uncle Sam,” 1900.
“Time for a new declaration,” John R. Fischetti, Collier’s, 4 July 1953.
And they’re often on the same side!
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For further reading (and images!), check out the US Library of Congress exhibit “John Bull and Uncle Sam: Four Centuries of British-American Relations.”
See also:
– Part II: Representations of UK & US Cooperation
– Part III: John Bull & Uncle Sam, a friendship to the end
Carto-Caricatures: Cartographic Caricatures 
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