He also made clear that there was little doubt that of three options being presented on the way forward - continue restoration on a piecemeal basis, having a more intense programme of work or move MPs out altogether to enable an army of workmen unfettered access - the latter was almost certain to be agreed.
The source said: "The initial estimate might be £1bn but it will be at least £2bn if not more. Look at what happened to the Scottish Parliament; its original estimate was £40m and it ended up being over £400m. These things always cost more in the long run."
Earlier this week, it was announced that Deloitte real estate would lead a consortium to undertake a £2m in-depth review of the repair and restoration programme. The hope is that by undertaking a highly detailed scoping exercise, future costs can be managed better and kept down. A final decision, which will involve a vote of both Houses, is not expected until after the 2015 General Election with any decant of MPs taking place after the following election in 2020.
Because such a major programme of repair and restoration has never taken place since the Palace of Westminster was built in 1860, no one is quite sure how long it will take. But the estimate is at least four years; a full parliament now lasts five. MPs could be moved to the Queen Elizabeth II conference centre.