Chancellor George Osborne has dropped plans to limit tax relief on charitable giving, after protests from charities.
He announced in the Budget a limit of £50,000 or 25% of income, whichever was higher, on the amount a person could donate instead of paying it in tax.
It is the latest in a series of changes to Budget policies this week, including the pasty and caravan taxes.
Charities welcomed the news of the change, but Labour called it another U-turn by a "shambolic" government.
Mr Osborne announced in his March Budget that from April 2013 there would be a maximum amount that could be reclaimed in tax relief - including on charitable giving.
The chancellor said in a newspaper interview he had been "shocked" by the scale of legal tax avoidance by the very rich, after seeing the result of a confidential study by HM Revenue and Customs and this was a "specific" loophole he wanted to close.
Downing Street suggested at the time that wealthy donors were giving money to charities that "don't, in all cases, do a lot of charity work" or operated abroad.
And setting out the plans in his Budget speech, Mr Osborne said: "Everyone in this country and particularly those with the highest incomes should contribute a fair share to the exchequer."
Under current rules higher rate taxpayers can donate unlimited amounts of money to charity, and offset it against their tax bill to effectively bring the amount of tax they pay down, sometimes to zero.
Although they are not benefiting financially, critics say it means they choose where their money is spent - unlike most taxpayers, whose cash goes to the government to fund things such as schools and hospitals.
The planned cap, which was similar to the rules as they apply in the US, was met with dismay by charities who claimed it would cause major donations to stop.
Announcing the rethink, Mr Osborne said: "I can confirm that we will proceed next year with a cap on income tax reliefs for wealthy people, but we won't be capping relief for giving money to charity.
"It is clear from our conversations with charities that any kind cap could damage donations, and as I said at the Budget that's not what we want at all. So we've listened.
"Frankly, at a time like this, the government is going to focus on the big issues like the worsening eurozone crisis and Britain's deficit, and not get distracted with unnecessary arguments. We're going to concentrate our efforts on what really matters: keeping Britain safe in the gathering storm."
The consultation on how a cap would be imposed on the other tax relief measures will continue this summer.
Sir Stuart Etherington, chief executive of the National Council for Voluntary Organisations, said: "This is a victory for common sense and validates the strength of feeling from the thousands of organisations who lent their weight to the 'Give it Back, George' campaign. This is a great day for philanthropy."
A spokesman for Macmillan Cancer Support said the government's rethink was a "sign of maturity" and it would benefit the community "greatly".
Tory MP and multi-millionaire Zac Goldsmith, who has been calling for a change of heart on the policy, said on Twitter: "Charity cap rethink is good news."
The artistic director of the National Theatre, Sir Nicholas Hytner, said he was delighted.
"It's pretty impressive to admit to having made a 100% mistake and to put it right so quickly," he told BBC Radio 4's the World at One.#
But Shadow Chancellor Ed Balls, for Labour, said the move called into question the government's economic judgement.
"Another day, another Budget tax u-turn - three successive u-turns in four days, all when Parliament is not sitting and just a few weeks after ministers were defending these measures, show just what an embarrassing shambles George Osborne's Budget has become."
Earlier this week, the government dropped plans to impose the full rate of VAT on hot food - dubbed the "pasty tax" - and static caravans after protests from bakers and caravan makers.
Using the Treasury's own estimates, the pasty tax U-turn results in an annual loss of revenue of £40m, the caravan tax a loss of £30m and the charitable giving U-turn £50m.
BBC Radio 4's The Report programme earlier this month questioned the suggestion charities might be hard hit by the change, after finding that many of the largest said they got about 1% of their income in donations over £50,000.
The programme highlighted areas that might have been hit, such as Cancer Research, and private schools who are often dependent on large donations for new facilities.