The size of the final increase remains a secret, although rumours abound that the original estimate of £2.25 million could more than double.
The organisation has also conceded that there is no chance that it will hit its original planned completion date, which was set for autumn of this year.
However, AF director Rowan Moore told the AJ that the foundation would be getting more for the extra money.
'The brief, cost and the ambition of the project have increased,' he said. 'I cannot tell you how much the final price will be, because that is currently being worked on. But the scale of the project is now bigger.'
He insisted though that there would soon be a planning application. 'We are at RIBA Stage D and are expecting a planning application to be submitted with Southwark in about a month's time.
'But it is now true that we will not complete in autumn of this year, which I am prepared to admit was always pretty over-ambitious,' he added.