The Treasury chief secretary appeared on The One Show to do his five-second imitation.
In a low-pitched voice, he said, "Of course my government has not created a financial and economic crisis," before smiling sheepishly.
The clip was filmed as part of a game for impressionist Rory Bremner, who had to guess who the cabinet minister was pretending to be.
It's not the first time Alexander has imitated Brown. BuzzFeed News understands he used to play the role of the then prime minister with Liberal Democrat leader Nick Clegg in preparation for Prime Minister's Questions.
Sources said Alexander, who was Clegg's chief of staff between 2008 and 2010, used to fire back retorts in a gruff voice ahead of the weekly bout.
Emily Ashton is a senior political correspondent for BuzzFeed News and is based in London.
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