A powerful alliance of aid groups, charities and arts organisations is launching a full-frontal assault on Treasury plans to limit tax relief for philanthropists, warning that they will have a devastating impact on the culture of giving at the heart of David Cameron's "big society".

The revolt – joined by organisations as diverse as Unicef, Macmillan Cancer Support, the National Theatre and the Royal Academy of Arts – comes amid signs of pressure from several cabinet ministers for a swift U-turn.

Charities and donors are also warning that a major "giving summit" in Downing Street next month will collapse as donors turn away, unless the measures, outlined in the chancellor's budget last month, are reversed.

As part of an assault on so-called aggressive tax avoidance – billed as a tycoon tax – George Osborne announced a limit on the amount of tax relief that wealthy donors could receive in respect of large donations. This would substantially cut the amount that philanthropists can claim back if they donated more than £200,000, meaning it would cost them far more to give the same sums to charities, aid projects, new hospitals, universities, arts bodies or other charitable causes.

David Bull, executive director of Unicef UK, said its work, including efforts to fight the effects of food shortages in Africa, could be seriously hampered. "Put simply, this new legislation will have the unintended consequence of discouraging donations to charity by philanthropists, leaving some of the world's most vulnerable children as the real losers." Unicef has already been warned by one donor who was lining up a six-figure gift that it may now be pulled because of the budget changes.

Nicholas Hytner, director of the National Theatre, said that since the budget his fundraisers had been contacted by a donor who had been considering handing over £250,000 to say he was having second thoughts.

Describing the tax hit on philanthropists as bizarre, Hytner said it ran directly contrary to everything else the government, particularly culture secretary Jeremy Hunt, had previously said on the need to encourage wealthy people to do more for civic society. "They specifically asked us to get our act together in our appeal to the very wealthy in order to cover the gap in our funding that had been created by the spending cuts," Hytner said.

In a letter to today's Observer Ciaran Devane, chief executive of Macmillan Cancer Support, says the cap will make it more difficult to fund projects such as its new cancer centre at University College hospital, London, which opened its doors to patients last week and will offer some of the best care in Europe.

Hunt, who published a white paper on how to encourage giving last year, is one of several cabinet ministers who have made their concerns known to Downing Street. He only found about the move on the day of the budget, fuelling suspicion that Osborne's package of measures to limit exploitation of tax reliefs was put together at the last minute.

Business secretary Vince Cable and David Willetts, the universities' minister, have both been heavily lobbied by vice-chancellors worried that funds from donations will dry up. Close friends of work and pensions secretary Iain Duncan Smith said he would resist moves that hit the charitable sector.

Former Liberal Democrat Treasury spokesman Lord Oakeshott, who gives large amounts to charity, described the policy as an example of "bad society, not big society", adding: "It's insulting nonsense to pretend people give generously to charity to dodge tax."

Charles Saumarez Smith, chief executive of the Royal Academy of Arts, said: "At a time when it is stated government policy to encourage more philanthropy to the arts, it is completely ridiculous to provide limits to the amounts that are given."

Currently, higher-rate taxpayers donating to a charity can reclaim a substantial proportion. From April, the maximum will be £50,000 per year, or 25% of the individual's income.

A spokesman for the chancellor said a rethink was not on the cards. He added, however, that Osborne had made clear he would "proactively explore with philanthropists ways to ensure the new limit [on reliefs] will not significantly impact upon charities that depend on large donations".

Sir Stephen Bubb, chief executive of the Association of Chief Executives of Voluntary Organisations, said there was no time for lengthy consultations as donors would pull away before it was complete. "The Treasury has promised a long-winded consultation, when the impact is already being felt. That is not what we need.

"The government must reverse this decision, and reverse it fast, if the anger of many charity leaders is to subside and vulnerable people here and abroad are not to pay the price."