Universities in England are preparing for cuts of more than £4bn in the government's Spending Review - with deep reductions in teaching budgets.
Universities UK has warned of "misplaced and mistimed cuts", with expected cuts of about £3bn for teaching and £1bn for research.
Schools have been promised that front-line spending will be increased.
But there have been warnings of cuts to support services and funding streams that are part of school budgets.
There are also expected to be shake-ups for education maintenance allowances and Sure Start early years projects.
Universities UK president Steve Smith said cuts of £4bn would account for the biggest change in higher education for more than 40 years - and would mean withdrawing state funding for teaching in many subjects.
Lord Browne's review last week recommended a sharp increase in tuition fees - but universities have been angered that the extra funding from fees look set to be used to fill the gap from cuts in public spending.
The 1994 Group of research-intensive universities said the country's economic recovery was being "put at risk by starving universities of investment".
"The government will have effectively transferred the responsibility for the future funding of teaching to students and graduates," says the Million+ group of universities.
Schools have been promised that their core funding will be protected from spending cuts.
There has also been a commitment to a pupil premium to help schools teaching disadvantaged children, which will rise to £2.5bn per year.
Education Secretary Michael Gove said this money, as part of a £7bn four-year package, "will be invested in accelerating social mobility".
'Hanging in the balance'
But teachers' unions have warned that they are "holding their breath" to see the details of changes to support services and other funding streams that supplement school incomes.
Head teachers say they are "very nervous of the funding reality" if they lose services outside this protected core budget.
"Schools will lose out if, for example, specialist school funding is axed, local authority services such as transport are cut, the capital fund for building repairs is chopped, or rising staff costs are ignored," says the ASCL head teachers' union.
They are worried that the "protected" budget for schools will still mean that they will lose part of their income, if other non-core funding streams are taken away.
For instance, more than 95% of secondary schools have specialist status, which adds £450m to their budgets and costs £16m to administer.
Speaking to the BBC's Today programme, Mr Gove said the schools' budget would not be cut, but the impact of budget changes would differ across the country and there would still be some schools where "efficiencies will be demanded".
Education maintenance allowances, received by about 600,000 young people aged between 16 and 18, could also face an overhaul.
These mean-tested allowances, worth up to £30 per week for families earning less than £20,817, cost £564m per year.
The Sure Start scheme, which provides centres and services to families of young children, has also been suggested as being likely to face changes.
A number of education quangos and regulators have already been scrapped - and other projects, programmes and administrative organisations could also be set to follow them.
Campaigners for disabled people have expressed fears over the impact of welfare cuts.
The disability charity, Scope, has warned of the "disabled being pushed further into poverty and closer to the fringes of society".
The National Autistic Society said lives would be "hanging in the balance" over funding decisions.
The charity warned that cuts to support and local authority services "may push whole families to crisis point".