The row highlighted a growing gulf between the Lib Dems and Conservatives who are pushing for the 45p rate for those earning £150,000 which the coalition brought down from 50p to be lowered again to 40p.
Mr Alexander, the most senior Scot in the cabinet, ruled out a cut in the top rate in March’s budget and insisted that he would veto any plans to reduce it before the 2015 election.
It follows Labour pledging to restore the 50p rate if they are elected at the next general election.
In a newspaper interview Mr Alexander said the 45p rate was the “right place to be” and any cuts will be “over his dead body”.
Mr Johnson, seen by many as the next Tory leader, has publicly pressed for the top rate to be reduced to 40p raising concerns that it was driving high earners away from London.
Speaking on the Today programme, Mr Johnson refused to rule out the possibility of the Government cutting the top rate of tax before the 2015 election.
Put to him that this would require the removal of Mr Alexander, the Mayor said: “Who can say what will happen to Danny Alexander? Stranger things have happened at sea.
“I don’t think it is reasonable always to keep UK tax rates higher than those of competitor countries.”