Sir David, the former London Olympics supremo, said HS2 was “vital for the future of the country”.
He added: “The cost and impact have to be recognised and acknowledged, but so too do the cost and impact of doing nothing.
“Without HS2, the people of this country will continue to face the failures of our transport system on a daily basis.
“This contingency has pushed the price of phase one – from London to Birmingham – up to £21.4bn with £3bn for the trains, while the cost of the second phase, taking the line in a Y-shape to north west and north east England is put at £21.2bn with around £4.5bn for the trains.
Not finished until 2032/2033
Phase one, which takes the line through Tory heartlands in the Chilterns to Birmingham, is set to be completed in 2026 while phase two is likely to be finished around 2032/33.