The insurance trade body said scrapping the MPAA would help savers who have had to dip into their retirement savings during the Coronavirus pandemic.
Removing the MPAA would mean they would not to be penalised for paying back into their pension when they can, the ABI said.
Scrapping the allowance would also incentivise older workers to continue to save into their pension, improving their financial resilience, according to the ABI.
The call to scrap the MPAA comes as figures from the ABI show that the number of people accessing their pension pots in December exceeded 2019 levels for the first time since the pandemic began.
The number of pension pots accessed as a flexible income increased 3% from 7,737 in December 2019 to 7,936 in December 2020.
The number of people withdrawing all their pension in one lump sum increased by 4% from 11,076 to 11,501.
The insurance body said that with unemployment at its highest since 2014, this could also lead to further increases in people accessing their pension in 2021.
Data from the Office for National Statistics on the labour market released on Tuesday showed the number of people unemployed aged 50 – 64 has increased by over 43% since the start of the pandemic from 276,000 to 395,000 people.
Yvonne Braun, director of policy for long-term savings and protection at the ABI, said the pandemic has shown that households’ financial resilience can be fragile and addressing that should be a “central part of the nation’s Covid-19 recovery”.
She said: “Our data suggests that pension withdrawals have not yet substantially increased but the continued uncertainty and insecure job market could mean more people dipping into their retirement savings to get by. Removing or increasing the Money Purchase Annual Allowance will help incentivise older workers to save. This will improve their financial resilience and also make sure people are not penalised for doing the right thing by paying money back into their pension when they can afford to.”