People retiring with modest pension savings are among the biggest victims of an annuities market that is failing consumers, the City regulator has warned.Savers with small pension pots have less choice than others when they retire and are offered inferior annuity rates, according to the Financial Conduct Authority (FCA), which said insurers had "closed the door on them".That damning verdict was one of several arising from an in-depth review of the annuity market that was published by the watchdog yesterday. It concluded that the GBP14 billion a year annuities market is "disorderly" and not working well for savers.Annuities are bought at retirement by some 420,000 people a year to convert their lifetime pension savings into a regular income.Six in ten annuities are bought through the existing pension provider or a connected third party. Of those who don't switch to a different provider, 80 per cent could get a better deal from doing so (equating to 320,000 people every year), the FCA calculated.It is now launching a competition study into the market to find out why so few people get a decent deal.The review found that people with small pension pots are among the biggest losers from the malfunctioning market.Martin Wheatley, chief executive of the FCA, said: "Our research showed that there is virtually no market whatsoever for people with smaller pension pots. This means that for those people who need to make every penny of their pension count, the market has closed the door on them."People with small pension pots are typically offered lower rates than those with larger sums - they tend to improve from around GBP10,000 - and have less choice of providers. Yet more than one in four annuities sold by pension firms to existing customers in 2012 were for funds worth less than GBP5,000, the FCA revealed.Almost a third of people buying annuities have pension pots of GBP10,000 or less, Association of British Insurers (ABI) figures show, with the average pension pot around GBP36,000.Just a tiny minority of firms offer annuities for this size of fund, however, and even then customers are rarely made aware of it.The absence of competition for low-value savings is because the profitability for insurers is negligible at that level, said Andrew Tully, pensions technical director at MGM Advantage."The fixed costs involved in setting up contracts have a disproportionate impact on small pots," he explained.Edinburgh-based Standard Life offers annuities on the open-market to savers with pots as low as GBP3,000. Its average pot size is around GBP12,500.Barry O'Dwyer, of Standard Life, said: "The stark fact is most people have insufficient savings and come to retire with small pots of money to convert into an income. Customers who take an annuity with us generally have small pension pots and some do have difficulty finding a choice of annuity providers who will take them on."The alternative for people with small pension savings is to take their benefits as cash lump sums, under a system known as trivial commutation. The rules can be complex and awareness of them is low, however, adding to the obstacles facing retirees.Trivial commutation allows savers aged 60 and over to cash in their combined pension pots for a lump sum, provided their total value is below GBP18,000. Up to 25 per cent of the lump sum can be taken tax-free.Individual workplace and personal pensions worth less than GBP2,000 can also be cashed in - up to a maximum of two pots for personal pensions - even where the total pension savings are above the GBP18,000 mark.But some insurance companies refuse to play by these rules and refuse to release "stranded" workplace pensions worth less than GBP2,000, according to advisers.Tully wants the government to help savers by relaxing the trivial commutation rules."Small pots are an issue as the current triviality rules are so complex. That's why we've called for a simplification of the triviality rules, and allowing people to take pots below GBP10,000 as a lump sum without reference to other pension saving"People would benefit from having a lump sum to use as they see fit rather than a very small income for the rest of their life."