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The British thriller “Plastic” is supposedly based on a true story, though — with the number of coincidences, contrivances and conveniences — that’s a little tough to swallow.

No matter. The attractive cast, the London and Miami settings and director/co-writer Julian Gilbey’s breezy style make it more enjoyable than enraging.

Ed Speleers (“Downton Abbey”) is Sam, a young man in recessionary England. He leads a crew of youthful criminals who purloin IDs and credit cards with impunity. But, when they steal something from the wrong guy — vicious mobster Marcel (Thomas Kretschmann) — things get ugly. He gives them two weeks to get him 2 million pounds or they’ll die brutal deaths.

Sam and his boys then put into motion their biggest heist yet, one involving a girlfriend (Emma Rigby) who works at a credit-card company and a trip to South Beach. If it works, they will pay off their debt to Marcel and have enough left over to move to “Easy Street.” That’s when the suspension of disbelief gets stretched to the breaking point.

“Plastic” may be no more real than the plastic these guys keep in their wallets, but its lightweight entertainment is not counterfeit.