But Transport Secretary Chris Grayling said the higher figure is "just nonsense".
Preparatory works are already underway, with main construction work starting in 2018/19.
Further HS2 announcements are taking place today which may clarify the exact route of the rail line as it moves further north.
Subject to Parliamentary approval this means that this part of the route can open in 2027, six years earlier than planned.
These include the details of the routes of Phase 2a between Birmingham and Crewe and Phase 2b between Crewe and Manchester and between the West Midlands and Leeds, to be revealed later today. This includes working with HS2 Ltd, Network Rail, the station design contract victor and local authorities to deliver a unified masterplan to unlock the full potential of the area.
Grayling said: "This is a hugely important step in the construction of Britain's new railway and underlines this government's determination to deliver an economy that works for all".
"HS2 offers transformational opportunities for the local, regional and national economy through job creation, better connectivity, shorter journey times, improved onward services to Scotland and freeing up capacity on existing lines, so is it vital it is delivered in full".
" We will now get on with building the railway, while continuing to ensure affected communities get appropriate support and are treated with fairness, compassion and respect".
David Higgins, Chairman of HS2 Ltd, said: "HS2 was always created to be much more than just a high speed railway and today we can see the opportunities it brings right around the country".
HS2 was always created to be much more than just a high speed railway and today we can see the opportunities it brings right around the country - spreading prosperity, acting as a catalyst for investment and rebalancing our economy 10 years before the railway even opens. Business now has the surety to invest with confidence to build a legacy for Britain.
Joe Rukin of Stop HS2 referred to the project once again as a "white elephant", saying "The case for HS2 has been invented by the very cheerleaders who intend to rake in billions of taxpayers' money which is desperately needed elsewhere".
Joe Rukin of the Stop HS2 campaign said: "The case for HS2 has been invented by the very cheerleaders who intend to rake in billions of taxpayers' money which is desperately needed elsewhere, so it really is time to ditch this big white elephant before it is too late".
In November a year ago, ministers said the line should serve the existing central station in Sheffield, after proposals to run trains to the Meadowhall shopping centre were set aside.
But this could see new homes in nearby Mexborough being pulled down, with numerous estate's residents finding out about the possibility just weeks after moving in.