Fiona Boulton, chairwoman of the Headmasters' and Headmistresses' Conference (HMC) accused "political activists" who want private schools to pay more tax of failing to understand the "common sense" of the British people.
Her comments come amid a growing row between the sector and the Labour party over the future of private schools.
Mrs Boulton is expected to tell the HMC's annual conference in London: "Voters want the government to help more children to get access to independent schools. Parents are ambitious for their children and people want to see our schools opening up, not closing down.
"This tells us that the policy of destroying great independent schools is a vote loser. The political activists who want to tax good schools to death without a notion of how to nurture achievement elsewhere, do not understand the common sense of the British people."
What the polls say
Her comments come as polling of UK adults, commissioned by HMC, suggested that many are in favour of allowing parents to pay for schooling.
Around two thirds (68%) of those questioned agreed that parents should be able to choose to pay for their child's education, if they can afford it.
Just under a fifth (18%) disagreed.
A breakdown by political affiliation shows that the vast majority (83%) of Conservative voters are in favour of allowing parents to choose, along with more than half (56%) of Labour voters and 70% of those voting Liberal Democrat.
Mrs Boulton, who is also head of the all-girls Guildford High School, will also reiterate private educators' fears that measures to impose "crippling taxes" is abolition of the sector "by the back door" and accused Labour of making "ignorant" decisions.
"Do not be fooled into thinking that imposing crippling taxes is anything other than abolition by the back door," she says.
"It would ensure that many independent schools would not survive, and others will become more expensive. State schools will see larger class sizes and burgeoning costs.
"The decision taken by Labour conference to abolish our schools was based on ignorance and the desire to damage, whilst independent schools have for years been quietly educating children, alongside creating free and discounted places, sponsoring successful academies and delivering more than 5,000 helpful projects in state schools' communities."
Private school proposals
Mrs Boulton says private schools have proposed to offer 10,000 free places to lower-income pupils each year, based on a joint-funding model, which would mean that the Government would contribute the same amount of funding as it costs to send a child to a state school, with the private school paying the rest.
Mike Buchanan, HMC executive director, said the survey "underlines the public belief that parents should be free to make choices for their children, including paying for their child's education rather than asking the state to do so."
He added: "It is striking that the findings suggest the public is in no mood to uproot a valued national asset, and many would like to see the benefits offered by independent schools made even more widely available."
Delegates at Labour's conference approved a motion which said a commitment to "integrate" private schools into the state sector should be included in the party's next general election manifesto.
This would include the withdrawal of charitable status and "all other public subsidies and tax privileges", including business rate exemption.
Properties and investment held by private schools would be "redistributed democratically and fairly" across the country's educational institutions as part of the reforms.
And universities would have to admit the same proportion of private school students as in the wider population, currently around 7%.
The vote in favour of the motion came after shadow education secretary Angela Rayner said a future Labour government would scrap the "tax loopholes" which benefit private schools, in its first budget.
Under current rules, private schools are eligible for charitable status, which means they can get tax breaks on things such as business rates. There is also no VAT on school fees.
In comparison, state schools are liable for business rates, which are effectively paid for by the taxpayer.
Academies - which are not under local council control - typically have charitable status and are therefore eligible for discounted rates, with the rest paid for out of their state funding.
Council-run schools have their business rates funded by the local authority.
Shadow education secretary Angela Rayner said: "Boris Johnson has broken his own election promise to rethink the tax privileges enjoyed by private schools, while the vast majority of children still face the impact of Tory cuts on their own education.
"Where the Tories have failed, the next Labour government will act, using our first Budget to immediately end the tax breaks gifted to private schools and reinvesting that money in our schools to improve the lives of all children, regardless of their background. We will end the absurd situation where every state school pays business rates but schools like Eton do not."
A Labour source said: "Of course the establishment will try to defend its privileges. But these are leading questions that don't tackle the real issues at all.
"We note that the private schools lobby failed to ask the British public whether they thought it was right that children's life chances are determined by how wealthy their family is, or whether
it is right that private schools don't pay their taxes like the rest of us."