Based on HMRC data, there were approximately 4.4 million higher rate taxpayers in the tax year 2013-14. Prudential's research indicated that one million of them were not contributing to any pension scheme.
Researchers said with average annual earnings of a higher rate taxpayer of £50,200, making pension contributions of five per cent this would reduce their annual tax bill by around £1,000.
In many cases they could also benefit from additional employer contributions to a pension scheme, they said.
The actual total amount of unclaimed tax relief could be even higher than this, according to Prudential's experts. Of those higher rate taxpayers who have been contributing to a pension, 23 per cent were unsure whether they were reclaiming the full tax relief on their pension contributions that they were entitled to.
Clare Moffat, a tax expert at Prudential, said: "While members of occupational pension schemes receive basic and higher rate tax relief automatically through their payroll, members of personal pension schemes, including Group Personal Pension Schemes, Self Invested Personal Pensions and stakeholder pensions, only receive basic rate 20 per cent tax relief automatically. Higher rate taxpayers who are members of these schemes have to claim the additional relief themselves, through their annual tax return or by informing HMRC.

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"A typical higher rate taxpayer who fails to claim this additional 20 per cent relief would effectively be surrendering £500 to the taxman, assuming typical earnings of £50,200 and contributions of five per cent.
"Overall, HMRC figures suggest the total tax liabilities for higher rate taxpayers is £62.7 billion a year, equating to an average tax bill of £14,3002."
Ms Moffat said: "Many people go to great lengths to make everyday household savings that could amount to only a few pounds.
"While that is not insignificant, they could bank many hundreds of pounds a year simply by fully utilising the tax relief available on certain pension contributions.
"With an annual average of £1,000 in tax relief available to higher rate taxpayers, it makes sense for people to maximise their contributions and make sure they're getting all the relief they are due.
"Additionally, those who make regular pension contributions will potentially receive valuable employer contributions and therefore benefit from an even greater boost to the eventual value of their retirement pot.