The planned pension charge cap should be reduced to 0.5% and extended to all funds, not just those used for auto-enrolment, according to Which?
The consumer group has launched a campaign - Hands off my pension - with the aim of pushing pensions minister Steve Webb to go further on his crusade against high charges.
Webb wants to see a charge cap of either 0.75% or 1% introduced for all auto-enrolment pension schemes, but Which? wants him to go further.
It said the cut from 0.75% to 0.5% would see thousands of pounds currently eaten up in charges turned into retirement income for savers.
The campaign also wants to see a ban on annual management charges being increased when people switch jobs.
Which? executive director, Richard Lloyd, said: "Millions of people are currently paying in to rip off pensions, but many might not realise so much of their money is being taken in fees until it's too late.
"While we strongly support the direction of the government's plans there is an urgent need for better minimum standards for all workplace pensions so people can be confident that they are being enrolled into high quality, good value schemes.
"With consumers being squeezed by the rising cost of living, there is no room for rip-off pension schemes in the workplace."
Hargreaves Lansdown head of pensions research Tom McPhail said the 0.5% cap would make a mockery of NEST's current charging structure.
At present NEST savers pay an annual management charge of 0.3% on the total value of their fund and a 1.8% charge on each new contribution.
McPhail explained: "A simple charge cap of 0.5% across the board would make NEST a ‘rip off pension', as anyone joining NEST for less than 16 years will end up paying more than 0.5% in total charges.
"This is obviously a ridiculous accusation, NEST is a very good pension scheme set up on competitive terms. Hargreaves Lansdown believes the focus should be on legacy schemes as market forces are already successfully at work on new schemes."
In a separate Which? investigation the group found a third (35%) of people who have opted out of auto-enrolment, or say they will opt out, do so because they do not trust the pension industry to look after their money, and one in five (22%) because they are concerned about the quality of the scheme.
Which? is asking consumers to support the Hands Off My Pension campaign and share their views via www.which.co.uk/handsoff
What made financial headlines over the weekend?
Compared to 6% of 55-64 years olds
Sam Gold and Doug Abbott to take reins
Bionic advice for private clients