Turns out Robert was born in Britain but was raised in America.
Robert is introduced drowning kittens in his teacup while snacking on crumpets with spread made from babies. Alice must stop him from taking over America with the help of the SAS and turning it into the world's largest Bangers and Mash factory.
Bobbie the cockney orphan is the only character without an American accent. He turns out to be The Man Behind the Man.
The director is aware that there is more than one British accent - and chooses the absolute goofiest ones for all the villains.
Alice tries to stop Robert from taking over the world...wait, it turns out he's innocent. Hang on, it looks like the real Big Bad has an accent anyway...nope he just put it on to mock Alice's assumptions about Robert. Wait, Robert's the Man Behind the Man...or is he...?
The evil British villains are working for an American. (For a more unusual twist, the Big Bad is, say, Belgian or Canadian.)
Averted: The cast is made up entirely of Britons or has no one with a British accent in it.
It's a movie about either the American or the Irish Revolution, at the very least the villain will probably be British.
Corollary: if an American movie is about a ragtag group of rebels against an Evil Empire the rebels will speak with an American accent and the baddies with a British accent.
"Good day chaps, did my accent give me away?"
"We Britons have a long history of supervillainy! Shall I give you a history lesson?"
Exploited: Robert blackmails William the Upper-Class Twit into being his stooge in the hope that his enemies will assume that William's the Big Bad based on this trope and won't investigate further (and trace it back to him).
Defied: Robert joins the heros solely to disprove this trope.