Universities UK head Professor Steve Smith wrote to vice-chancellors saying this week's Browne Review set out figures that "confirm our worst fears".
He says they signal a £3.2bn or 79% cut from teaching and £1bn from research in next week's Spending Review.
The government said it could not comment.
This is because the Department for Business, Innovation and Skills said it could not speculate about the Chancellor's spending review plans.
Currently universities are given around £11bn in government grants a year - this covers undergraduate and post-graduate teaching, research funding and infrastructure.
The UCU lecturers' union said cuts of the order being discussed would lead to university closures while the National Union of Students warned the government was stripping away the public funding of universities.
In his letter to fellow vice-chancellors, the UUK president suggests the impact of the Spending Review will be more important than Lord Browne's review of fees published this week.
This is "because potential cuts have been getting worse and worse", he says.
He continues: "Browne explicitly says that Hefce (England's university funding body) will have teaching funding of £700m; the current sum is £3.9bn.
"This implies a cut of around £3.2bn in state funding."
This would represent a 79% cut in the teaching grant.
He adds: "Browne's figures confirm our worst fears. Cuts in the order of £1bn for research also appear to be proposed."
A £4.2bn cut in funding would be almost four times that which universities had been expected to make by the previous government.
Professor Smith says the Browne report, which itself called for unlimited tuition fees, was framed by "what is coming on October 20".
And he adds that universities will do all they can to "replace as much of this lost funding as possible". This means raising tuition fees to make up for lost state funding, he says
But he also warns that this may not be possible before 2012, when the government is expecting to have measures in place to allow for a rise in fees.
He adds: "The biggest worry is simple to state: if Browne fails to get through the Commons, or gets unpicked, or gets accepted but only after major changes are made, we will simply not be able to replace the unprecedented reductions in state funding that are coming in the Spending Review."
Responding to the claim, the general secretary of the UCU, Sally Hunt, said: "It is hard to believe that any government could contemplate making £4.2bn cuts to higher education given that it generates massive economic growth.
"Cuts of this magnitude will leave many cities and towns without a local university and our students paying the highest public fees in the world."
She called for an urgent review of the impact of "these unimaginable cuts".
President of the NUS Aaron Porter said: "The devastating scale of the cuts to publicly funded degrees planned for next week is laid bare by this admission.
"The true agenda of the coalition government this week is to strip away all public support for arts, humanities and social science provision in universities and to pass on the costs directly to students' bank accounts."
He accused vice-chancellors of standing by plans that would lead to many universities closing down.
A spokesman for the Department for Business, Innovation and Skills dismissed the figures as speculation
He added: "Lord Browne made recommendations to government this week on a new funding system. His proposals are for graduates to make a greater contribution to the cost of their education, linked to their ability to pay.
"These recommendations are currently under consideration and are informing our comprehensive spending review negotiations with the Treasury. Ensuring the university sector is properly funded remains a key objective for the government."
But Shadow Business Secretary John Denham said the coalition was clearly planning unprecedented cuts in higher education.
"It will mean pushing all or most of the cost of the university education onto students.
"For Britain in a global economy it will damage one of the main drivers of growth, jobs and prosperity," he added.