The warning that it was over budget was given in May 2016, two months after legislation for the first stretch of the line was approved by MPs, according to the BBC.
Last week, a Government-commissioned review into whether the scheme should continue was launched amid growing fears it cannot be built to its current specification within its £55.7 billion estimate.
The BBC reported it has seen a May 2016 letter written by then-transport secretary Patrick McLoughlin to George Osborne - chancellor at the time - stating that the first phase between London and Birmingham - originally costed at £24 billion - was £1 billion over budget.
A “confidential” DfT briefing report from December 2016 also stated that “a significant gap to target price will remain” for HS2 even with planned savings.
There has been increasing concern over its spiralling cost, with warnings that the final bill could reach as much as £85 billion.
However Transport Minister Nusrat Ghani told the Commons last month that “there is only one budget for HS2, and it is £55.7 billion”.
The Transport Salaried Staffs’ Association, which represents workers in the transport and travel industries, said it was no surprise that the Conservatives “knowingly underbudgeted”.
Manuel Cortes, TSSA General Secretary, urged the Government to use the review to rebudget - and take HS2 “all the way to Scotland”.
“They can find enough money to buy the DUP’s support over Brexit but they try to get everything else done on the cheap,” he said
“But we mustn’t lose sight of the many benefits that HS2 will deliver the environment – taking cars and freight off our roads – and regional economies the length and breadth of the UK.
“Contrary to what Boris and his pals seem to think Britain is more than just London and the Home Counties.
“HS2 is a golden opportunity to boost regional economies across the country, to create more jobs and better connect cities.”
Meanwhile Andy McDonald MP, Labour’s Shadow Transport Secretary, said trying to hide the cost was “dishonest and bound to fail”.
He added: “Now is the time for the Conservatives to provide transparency on HS2’s finances and governance.”
Phase 1 from London to Birmingham is due to be completed by December 2026, while a second Y-shaped phase will launch in two stages.
Phase 2a from the West Midlands to Crewe is due to open in 2027, followed by Phase 2b from Crewe to Manchester, and Birmingham to Leeds, in 2033.
A Department for Transport (DfT) spokesman said HS2 is Europe's biggest construction programme and "like all major, complex projects, delivery plans evolve over time".
An HS2 Ltd spokesman said the scheme had come under “extensive scrutiny” including studies and reviews by the NAO and parliamentary committees.
He went on: “Since 2016, we have moved a long way as a project and organisation.
“We have now appointed a set of world-leading civil engineering contractors which enables us to have greater confidence about cost and construction schedules, as well as making significant changes to our management team.
"Our CEO has spoken publicly for some time about the cost pressures facing the project and we are working closely with our contractors to bear down on cost before major works commence.”