American Jack Lemley has also said he urged Jowell and the chief executive of the government's Olympic Executive, Jeff Jacobs, to go public with this knowledge. But he said his pleas had been ignored and that he had effectively been silenced by the minister.
'These numbers have been known for months by everybody,' he said. 'And if Tessa Jowell hasn't told the Prime Minister then she wasn't doing her job.'
Jowell is said to be furious with the comments, and has said Lemley is 'trying to rewrite history'.
In a statement, Jowell's Department of Culture, Media and Sport said: 'On costs, we, not he, initiated a full-scale cost review. It was certainly not the case that Mr Lemley was prevented from speaking at the Olympic board.
'In fact, as ODA chair the board expected him and the chief executive to provide regular progress reports and to bring forward key decisions for approval.'
This is the second time Lemley has taken a pot shot at his former colleagues since he stood down from the ODA. The first followed his resignation in October, when he claimed the games had been dogged from the start by political infighting and spiralling costs.