Funding problems delivering the new 10-storey building, where Mace is construction manager, were revealed by Tate director Sir Nicholas Serota while unveiling the annual report.
He said he was confident the new gallery building would open in June next year in spite of a shortfall of about £30m in capital funding for the project.
Tate Modern fund raisers are now on a final push to raise money over the next six months.
Serota blamed the 21% cost overrun on high building cost inflation and a decision to extend the scope of the project to refurbish parts of the main gallery.
In 2006, it was projected that the new building would cost £215m at 2012 prices and was originally due to be completed in February 2012.
Last year the Tate drafted in Stanhope to find ways of keeping the project on track amid fears of further delays and budget overruns.
When completed the brick-clad extension building will connect to the existing galleries of the six-storey boiler house, putting the main turbine hall at the heart of the new Tate Modern complex.
