The critically-acclaimed drama, created by writer and producer David Simon, shows life in Baltimore from different view points including those of drug users, politicians and local journalists.
Drugs investigation
West, who plays maverick police officer Jimmy McNulty in the show, said: "I love costume drama, no-one does it like the BBC - no-one has the money to do it, first of all and, secondly, Americans don't have the history to do it.
I thought Cranford was incredible but we don't seem to be able to do contemporary stuff
Dominic West
"So we do it brilliantly but if you talk to any BBC producers, they abhor the fact... they're dying to do The Wire and hate doing Cranford."
He added: "I thought Cranford was incredible but we don't seem to be able to do contemporary stuff."
In response, the BBC said a wide variety of dramas are made "of which period is a tiny proportion" and to suggest that producers "hate" working on such pieces "is nonsense".
The Wire's first season follows a police drugs investigation and features the stories of officers and their targets.
The entire five seasons, comprising 60 episodes, will be shown on BBC Two.
Sue Deeks, the BBC's head of programme acquisitions, said it was "a wonderful chance for everyone to see what the critics have been raving about for so long".
The show previously aired in the UK on pay TV channel FX.
The Wire will appear on BBC Two on Monday at 2320 BST.
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