It recently emerged that the corporation had scrapped plans to relocate from their current base in Elstree to the East End from 2012.
Culture Secretary Jeremy Hunt held unsuccessful last minute talks with BBC director general Mark Thompson, according to the Evening Standard.
Johnson exclaimed: "This was an opportunity for the BBC to deliver better value for money for hard-pressed licence-fee payers and confront critics who say it's bureaucratic, wasteful and out of touch.
"There was the chance for the BBC to show genuine commitment to the East End - an area it has harvested for audiences for decades. I'm astonished that the boss class don't see the obvious advantages of rooting a popular drama in an area it claims to portray."
Meanwhile, the 47-year-old politician also criticised the supposed "relentless negativity" in EastEnders' storylines.
"Perhaps if they seized this opportunity their plots and script lines would reflect the vibrancy and optimism of this critical part of the capital and not the relentless negativity that often comes across," he added.
A BBC spokesman confirmed to property website CoStar News: "EastEnders is committed to Elstree and there are no plans to relocate any time soon. We are not currently in active negotiations with any party."
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