The reduction of the annual allowance in 2014 has caused a significant rise in the number of people breaching the limit.
In the 2014/15 tax year - the last date at which the data is available - 7,000 people had reported on their tax return that they had breached the limit of £40,000. This is up 79% from 3,900 people in the 2012/13 financial year, when the allowance was £50,000.
The information was revealed in response to a Freedom of Information (FOI) request to HM Revenue and Customs (HMRC) from Royal London.
The data is compiled biennially and the 2016/17 year is expected to show a further increase, particularly due to higher earners seeing their limit tapered down to £10,000 since April last year.
Royal London's director of policy Sir Steve Webb said people may need to reduce their contributions to escape a large tax bill.
"Pension tax relief has been squeezed year after year, and these new figures reveal a big growth in the numbers paying a tax penalty for being over the annual allowance limit," he said.
"With a big cut in annual allowances for high earners in 2016/17, many more people risk breaching the limit unless they cut back on their contributions or use up unused allowances from earlier years."
Sir Steve said savers should take advantage of any unused allowance from the 2013/14 financial year - when the limit was £50,000 - over the next month, before the ‘carry forward' option expires on 5 April.
"Savers have just a few weeks to use up spare allowances from 2013/14," he continued.
The warning comes ahead of this week's Spring Budget, when the chancellor could tighten tax relief and the annual allowance yet again.
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