The extent of tax avoidance by Britain's super-rich has been revealed with the release of Treasury figures showing that almost a thousand UK taxpayers earning more than £1m a year have a tax rate of less than 30% of their income.

In an effort to get back on the political front foot over the budget, including its plans to impose a cap on tax reliefs, the Treasury also revealed that of the 200 taxpayers earning more than £10m a year, 12 are paying less than 10% in tax.

It is the first time the Treasury has published such comprehensive figures showing the tax rates of the super-rich. The figures formed the backdrop to the chancellor, George Osborne's recent admission that he had been "shocked" at statistics shown to him revealing the way in which the British super-rich use reliefs and legal schemes to avoid tax.

The Treasury has been on the defensive for more than a week over plans announced in the budget to cap the relief philanthropists can receive for charitable giving. Under the plans, to be introduced from 2013, previously uncapped tax reliefs – including on charitable donations – would be capped at £50,000 or 25% of income, if higher. The plan – billed ahead of the budget as a populist tycoon tax – has since gone disastrously wrong, as the Conservative press reported the plan as an assault on charitable giving.

The proposals – under repeated assault from universities, charities, philanthoposts and church leaders – suffered a fresh setback on Sunday night when the Charities Aid Foundation published a survey showing two-thirds of government backbenchers were opposed to the plans.

The new Treasury figures show 10,000 UK taxpayers earn between £1m and £5m, and, of those, 10% pay between 30% and 40% in tax, 5% pay between 20% and 30% tax, and 3% pay less than 10%.

The Treasury estimates that 400 taxpayers earn between £5m and £10m, and 5% of these taxpayers, or 20 individuals, pay less than 20% in tax.

Of those earning between £250,000 and £500,000, 27% were paying tax of less than 40%. All the figures cover the financial year 2010-11.

A Treasury spokesman said: "At the moment there are millionaires paying a lower tax rate than ordinary taxpayers. This is the system we have at the moment, but the government is committed to making it fairer. We're capping benefits and these figures clearly show why it's fair to cap tax reliefs for the wealthy as well."

Treasury sources pointed out the figures reflected a tax system inherited from Labour.

The sources also insisted the budget had been clear that real philanthropy would not be hit and the next year would be spent working with the philanthropic sector and charities on the details.

The Treasury added that ministers wanted to create a US-style culture of giving, pointing out that the Americans achieve this despite having minimum rates of income tax for wealthy people and caps on reliefs.

But the Treasury denied reports that it was going to follow the US tax system precisely to provide relief on lifetime legacies.

The Charities Aid Foundation said its investigation showed two-thirds of government backbenchers surveyed during the Easter recess said tax relief on charitable donations should be exempt from the cap announced in the budget and that the government should review its proposal.

Of the Conservative and Liberal Democrat MPs surveyed, 65% agreed that "tax relief on charitable donations should be exempt from the proposed cap", while 68% of the backbenchers surveyed agreed that "the government should review its proposal to apply this cap on tax relief for charitable donations".

The ComRes survey also showed that 93% of coalition backbenchers agreed that the government "should do all it can to use the tax system to encourage charitable donations from wealthy donors".

John Low, the chief executive of the foundation, said: "The government now needs to listen and act on this clear message from coalition backbenchers – as well as from ministers, charities and donors – and reverse this ill-thought-through tax change."

Former prime minister Tony Blair joined the debate over the role of philanthropy. In a speech in the US, he said: "The best philanthropy is not just about giving money but giving leadership."The best philanthropists bring the gifts that made them successful – the drive, the determination, the refusal to accept something can't be done if it needs to be – into their philanthropy.

"It is creative not passive; it seeks to disrupt not follow conventional thinking. It steps into areas government is too fearful or too risk adverse to go. It uses technology and its power to change the world in innovative ways."