At the moment, people over the age of 65 are not taxed on the first £10,500 of their income, but this will be frozen for existing pensioners and from next April new pensioners will have a tax-free allowance of £9,205, bringing them into line with the general population.
Around half of pensioners will be affected by the changes, which will raise around £1 billion annually for the Government.
The average loss for pensioners has been put at £80 a year, rising to £197 for those retiring from next April.
Saga director-general Ros Altmann said: "This is an outrageous assault on decent middle-class pensioners.
"This Budget contains an enormous stealth tax for older people. Over the next five years, pensioners with an income of between £10,500 and £24,000 will be paying an extra £3 billion in tax while richer pensioners are left unaffected.
"There is nothing in this Budget for savers, there is nothing to improve the annuity market, nothing to appease the damage of quantitative easing and nothing to support Isa changes and shelter older people's money in cash.
"This Budget is terrible news for pensioners."
The move will save the Treasury £360 million next year, £670 million in 2014, more than £1 billion in 2015 and £1.25 billion in 2016.
A statement from the Treasury said: "We are taking a decision that the best way to help pensioners is through the triple lock, guaranteeing increases in the state pension.
"There is a goal of a simpler tax system and a simpler personal allowance system."
Chancellor George Osborne said the current age-related allowances were a "particularly complicated" feature of the tax system, which many pensioners do not understand, requiring around 150,000 pensioners to fill in self-assessment forms.
He said: "So over time we will simplify the tax system for pensioners by doing away with the complexity of the additional age-related allowances for anyone reaching the age of 65 on or after April 6 2013 and I will freeze the cash value of the allowance for existing pensioners until it aligns with the personal allowance.
"This will protect the existing level of allowance pensioners have, while introducing a single personal allowance for all."
But TUC general secretary Brendan Barber said: "The Chancellor's decision to raise more than a billion extra pounds in tax from pensioners by freezing age allowances will come back to haunt him. It's already being dubbed 'the granny tax'.
"Pretending that pensioners will be grateful because it will simplify their tax is a vain hope. Instead they will see that they are being asked to pay more while the super-rich have kept all the pensions tax relief - a heavy burden for ordinary taxpayers.
"And with ever more increases in the state pension age threatened in a new White Paper - a burden that falls more heavily on the poor, the regions and those with manual jobs - older workers and pensioners are paying a heavy price for a pro-rich Budget."
Joanne Segars, chief executive of the National Association of Pension Funds (NAPF), said pensioners were the "biggest losers" in the Budget.
She said: "This will come as a blow to millions of pensioners who have paid into the tax system throughout their working lives."
But she welcomed the Government's plans to introduce a simple, single-tier state pension of around £140, based on contributions.
The Chancellor confirmed the introduction of a single-tier pension for future pensioners, which he said would cost no more than the current system in any year and represented "a further major simplification of our tax and benefit system".
The plans come ahead of a huge overhaul of the pensions system with the automatic enrolment of up to 10 million workers in schemes from this autumn.
Ms Segars said: "The new state pension will take millions of people off means-tested benefits. It will encourage people to start saving and to save more for their old age.
"A simple, more generous state pension will be a major step forward in tackling the nation's pensions crisis. And it will ensure that auto-enrolment, due to start later this year, is a success."
Further details about the new single-tier pension will be given by the Government later this spring.
The Government also signalled that the age of retirement will continue to creep up, with plans for an "automatic review" of state pension age to ensure it keeps pace with people living longer.
MGM Advantage found that official figures have shown a 4.2 year increase in life expectancy over the last 20 years for a 65-year-old man.
It said if this pattern is repeated, the state pension age could be 69 by 2031 and 73 20 years later.
Andrew Tully, pensions technical director at MGM Advantage, said: "This should serve as a wake-up call for many people.
"Today's 33-year-old is likely to need to work until age 73 before they get their state pension. They may have planned to work to age 65, but the reality is likely to be beyond age 70 for many."
John Lawson, head of pension policy at Standard Life, said: "If after 2026 the state pension age increases in line with our changing life expectancy, we could expect that someone who is currently 37 won't be able to start drawing their state pension until they are 70 and someone who is 21 won't receive it until they are 75.
"This means that children born in 2012 are unlikely to get their state pension until 80, if life expectancy at retirement rises in line with the last 30 years."
Chris Aitken, head of financial planning at Investec Wealth and Investment, said: "For us the most important part of the Budget was what it didn't contain, namely the reduction of tax relief on pension contributions for higher-rate taxpayers.
"We have an ageing population and to abolish this incentive to save for the future would be idiotic. The Government seems to have come to its senses on this, but we note that as ever the wording of the Chancellor's statement gives him the wriggle room to come back to it."
SNP work and pensions spokeswoman Eilidh Whiteford said: "The Budget truly fails the fairness test when millions of pensioners are penalised while millionaires get a tax cut from the Tories.
"While, as expected, the Chancellor increased personal tax allowances, his decision to freeze the higher age allowances granted to those aged over 65 will hit pensioners hard.
"The devil is always in the detail with Treasury announcements, and the Chancellor must now say whether any assessment was made of the impact of this decision on pensioner households."
Geraldine Bedell, editor of social networking site Gransnet, said the announcements were already being dubbed "the granny poll tax".
She said: "The Chancellor is in danger encouraging a new era of grey activism."
Shadow chancellor Ed Balls said many people would not have realised from Mr Osborne's speech that he was announcing a tax increase.
He said: "You thought from the Chancellor this was going to simplify personal allowances for pensioners in a way that would make it clearer to people who are confused.
"You didn't realise, in his speech, unless you know what you're talking about, he was actually announcing a tax rise."
Chief Secretary to the Treasury Danny Alexander said the Government was implementing the "largest increase ever" this year in the state pension.
The freeze in the age-related allowance was "a necessary simplification as we get the basic personal allowance up to the level of
the age-related allowance", he told BBC Radio 4's PM.
"I think it is a fairer system to have the same income tax personal allowance for everybody in this country," said Mr Alexander.
"Within the context of everything that we are doing for older people, I think it is a fair change."
But his Labour shadow Rachel Reeves said: "George Osborne has tried to bury his £3 billion 'Granny Tax' raid on pensioners over the next four years. The freeze in the personal allowance for pensioners will see 4.4 million pensioners who pay income tax losing an average of £83 per year next April. And people turning 65 next year will lose up to
£322.
"And he added insult to injury by dressing up a tax grab as a 'simplification' and claiming that he was taking this money away from pensioners because they could not understand the allowances they were entitled to."
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PA
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