Cultural projects including the British Museum's new exhibition wing and the redevelopment of the Tate Modern are under threat because of a £100 million black hole in Government funding.

The Department for Culture, Media and Sport has been criticised as "hopeless" for failing to spot the shortfall, which could force major arts schemes to be delayed or abandoned.

The nation's most prestigious galleries and museums have been sent a letter warning that tens of millions of pounds of Government capital investment will have to be clawed back to plug the deficit.

Funds earmarked for the Stonehenge visitor centre in Wiltshire and the British Film Institute's film centre on the South Bank in London may also be cut.

"It's hopeless management. Everyone will blame the DCMS for being hopeless, and they are fairly hopeless, so it's not unjustified," said one arts sources quoted by The Guardian.

Ministers have been warning arts leaders that funding previously promised funds for landmark projects are no longer guaranteed since the black hole was discovered a few weeks ago.

The DCMS last night confirmed that savings would have to be made but declined to explain how the department managed to exceed its budget by £100 million.

"Our capital budget is currently overcommitted. Ministers are examining the reasons for this and looking for solutions. It is possible that difficult decisions will be needed, but none has been taken yet," a spokeswoman said.

The Government has committed £50 million to the Tate Modern extension, which is intended to increase the size of the capital's leading modern art gallery by 60 per cent.

The British Museum has been pledged £22.5 million towards a new wing to house temporary exhibitions, but both these grants are now under review.

"There are too many schemes bidding for too little money," Barbara Follett, the culture minister, said last week.