George Osborne announced at the Budget on Wednesday that the allowance would be dropping from £1.25m to £1m from 2016 but said it would only hit the wealthiest few.
He said that fewer than 4 per cent of pension savers currently approaching retirement will be affected.
Mr Osborne said this move will save around £600m a year and from 2018 the Government would index the lifetime allowance.

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But David McKendrick, partner and Financial Planner at Cheshire-based Equilibrium Asset Management, said it would impact more widely.
He said: "The Chancellor's pension's lifetime allowance reduction is particularly harsh considering it was at £1.8m in 2012.
"Many people believe it will only impact the big high earners, but that simply isn't the case. The reduction will affect many ordinary workers as well. For example, a well-paid teacher who works all their life could easily accrue up to £1m in their pension pot.
"I think the allowance should be left alone and the Government is going to have to think carefully about any index it introduces."
Mr McKendrick, formerly of RPG Financial Planning, said: "To make pensions worthwhile to savers the index will have to increase more than inflation otherwise it will have no benefit. My advice to the Treasury is that the index should track inflation, plus 2 – 2.5 per cent and capped at 5 per cent."
Jason Hollands, managing director at Tilney Best Invest, agreed, saying: "While to most of us £1 million seems a tremendous sum, the reality is that after withdrawing 25% of a pension fund as a lump sum, which most retirees do these days, a residual pension fund of £750,000 would only provide a retirement income of between £18k to £21k per annum depending on the annuity selected. This is way below the national average earnings.
A great many public sector professionals who are still benefitting from final salary pension schemes, may be unpleasantly surprised to find themselves impacted, as they are unaware that the equivalent value of their pension pot will be in excess of £1 million."
Middle class professionals who are midway through their careers and are still some way off achieving a £1 million pension pot will also have to consider the impact, he said.
Towers Watson said the cut means that its value will have fallen by more than half in real terms since 2010.
The firm believes that people with defined contribution pension savings below £1 million could stop making contributions or invest more conservatively to avoid a tax charge.
Jackie Holmes, a senior consultant at Towers Watson, said: "In cash terms, the Lifetime Allowance has been reduced from £1.8 million in 2010 to £1 million in 2016. Once you take account of inflation, its real value will have more than halved.
"As with previous cuts to the Lifetime Allowance, people who already have pension pots worth more than £1 million will be protected – but for higher earners who haven't already done their pension saving, it will be too late."