He also said that speculation the Birmingham-Manchester leg of the route will be axed is also “deeply worrying”.
Sunak has refused to guarantee that the trains will run to Manchester, where the Tory conference is being held in October, and he could also look to make savings in the capital.
More than 80 companies and business leaders are seeking clarity over the commitment to HS2, the cost of which are said to be “out of control”.
A Whitehall source told the Sunday Telegraph: “There is a reluctance to throw good money after bad.”
Upper budget estimates of the initial London to Birmingham stretch have increased by a fifth – or more than £8bn – from the £45bn figure published in June last year and are on course to wipe out other transport projects, the newspaper said.
Former Prime Minister Boris Johnson has urged the government against building a “mutilated” version and said suggestions construction started under his premiership could be scaled back were “Treasury-driven nonsense”.
Ex-PM David Cameron has also privately raised significant concerns about the prospect that the high-speed rail line could be heavily altered, according to The Times.
In a letter to the Prime Minister, the Labour mayor said: “The Government’s approach to HS2 risks squandering the huge economic opportunity that it presents and turning it instead into a colossal waste of public money.”
Downing Street has refused to guarantee the HS2 railway line will run to Manchester as planned amid reports Rishi Sunak and Jeremy Hunt are in talks about scrapping the project’s second stage (PA)
/ PA Media
When the railway first opens between London and Birmingham, expected between 2029 and 2033, its terminus in the capital will be Old Oak Common, in the western suburbs.
HS2 trains are not expected to run to Euston until 2041 at the earliest and, with ministers concerned about the cost of the project, there are doubts the scheme will ever go ahead.
Khan said: “Terminating the service at Old Oak Common would be a short-sighted decision which will have long term implications, significantly downgrading the value of HS2 as a high-speed connection and leaving a ridiculous situation where a ‘high speed’ journey between Birmingham and central London could take as long as the existing route, if not longer.”
He said the “best case” journey time of one hour and 22 minutes from Birmingham to Euston, changing at Old Oak Common onto the Elizabeth Line and Northern Line, was “already one minute longer than the existing train time”.
Khan told the Prime Minister: “The public would rightly be dismayed were all of this time and money spent on a line that took longer to reach central London than the existing route, and was devoid of any proper connections to the north of England.”
A Government spokesman said: “The HS2 project is already well under way with spades in the ground, and our focus remains on delivering it.”