Royal London made the calculation after making a freedom of information (FOI) request to HM Revenue and Customs (HMRC).
When the "marriage allowance" was introduced in 2015/16, it was estimated that 4.2 million couples stood to gain.
But the FOI response received by Royal London showed that only 2.2 million couples have so far claimed - suggesting around two million couples could still benefit.
The allowance aims to help married couples and members of civil partnerships where one partner pays standard rate income tax and the other is a non-taxpayer.
The lower earner can transfer any unused tax-free allowance of up to 10% of the value of the full personal allowance to their higher-earning partner.
Assuming each couple took advantage of the ability to backdate to 2015/16, two million couples could potentially have £230 a year they are missing out on - and £662 each to gain overall.
Collectively, this could produce a total tax saving to consumers of more than £1.3 billion.
Sir Steve Webb, a former pensions minister who is now director of policy at Royal London, said: "The take-up of the new allowance is shockingly low. Even in its third year of operation, around two million couples who could benefit from the marriage allowance are not doing so.
"When family finances are so tight, I would encourage every married couple to check whether they might be eligible, including for the last two years, as they could qualify for a useful lump sum as well as a reduction in their ongoing tax bill."
A Government spokesman said: "2.2 million couples across the UK are keeping more of the money they earn thanks to the marriage allowance.
"Applications have increased year-on-year, the application process is easy and families can apply when convenient for them."
:: More information about the marriage allowance can be found at www.gov.uk/marriage-allowance.