Mr Johnson goes on to spell out his objections to the current plan - including "significant environmental concerns", particularly moves to send the route at ground level through Ealing and on a an elevated section at Hillingdon.
"It is perverse that a section of the route through Greater London, clearly affecting large numbers of people, has been subject to so little environmental mitigation.
"I am seeking substantial changes in design of the route to ensure these impacts are properly addressed, preferably by tunneling the whole route through London.
"Without such changes I cannot support the current proposal."
The Mayor complains that HS2 will lead a doubling of the current number of passengers arriving at Euston station every morning and that the Underground will not be able to cope.
"I wanted a commitment from the government that their proposals for HS2 would include new underground rail capacity between Euston and Victoria," he writes. "Thy do not and on this basis I cannot support the current proposal."
Mr Johnson also says the planed HS2 station at Old Oak Common in North West London will not be properly "plugged in" to the capital's infrastructure.
If ministers do not meet Mr Johnson's demands, and his objections to the project continue after negotiations, it could mean massive delays or even the scuppering of HS2, whose first phase is planned to run from London to Birmingham, with to further northern "spurs" reaching Manchester and Leeds.
Mr Johnson, who will fight Labour's Ken Livingstone in mayoral elections next year, has annoyed Mr Cameron by picking a series of fights over key issues of government policy - of which HS2 is the latest.
Mr Cameron's supporters have accused him of "political positioning" in a bid to be best place to succeed the Prime Minister as Tory leader.
The Mayor has clashed with the Prime Minister over Europe - by calling for a referendum on the Lisbon treaty - and on immigration by publicly objecting to moves to moves to put a "cap" on the number of people allowed into Britain from outside the European Union.
Mr Johnson said this was bad for business, a claim he repeated when he objected to the continuation of the current 50p top rate of income tax for higher earners. He also claimed coalition plans to curb housing benefit could lead to "Kosovo-style social cleansing" in London.
Many in the government object to Mr Johnson's call for strikes only to be legal if 50 per cent of a workforce have taken part in a ballot, while in October last year Mr Cameron declared thee government had "no plans" to build an airport in the Thames estuary area.
Most recently, the Mayor attacked plans - subsequently abandoned - by Ken Clarke, the Justice Secretary, to let criminals off half their sentences in return for guilty pleas.
Mr Marshall said: "The Mayor has raised serious and sensible questions about the impact on London of this eye wateringly expensive project.
"The Government's refusal to acknowledge these issues shows how fearful they are that cost will rocket still further. As the true extent of the disruption and costs becomes clear the tide of opposition is growing."
A Department for Transport spokesman said: "London's economy stands to benefit from the improved connectivity and increased capacity HS2 has to offer – that's why the capital's business community strongly supports the scheme.
"While our proposals for high speed rail will obviously have an impact on those communities directly affected, we are absolutely committed to doing everything possible to mitigate this."
The £34 billion HS2 link is the government’s flagship transport infrastructure project, enthusiastically promoted by ministers as boosting the economy and helping end the north-south divide.
It is expected to cut journey times from London to Birmingham by up to 30 minutes, to Manchester by up to 45 minutes and to Leeds by up to an hour.
Philip Hammond, the Transport Secretary, has pledged that the government will sell the line to private investors to recoup a large part of the taxpayer’s investment in the line, which is planned to begin operating around 2025.
Campaigners, however, claim it is an expensive white elephant being planned at a time of massive Government cuts to public services.
John Redwood, the former Conservative cabinet minister, has said the line is a “luxury we cannot afford at the moment”. In addition, ministers have faced protests from those living along its proposed route, including from Tory donors.
Labour supports the scheme on principle but has called for “more clarity” on the precise costs.