Providers such as Prudential, Standard Life, Partnership and Just Retirement say some people will be hit by RPI deflation which now stands at -0.4 per cent.
Less than 10 per cent of annuities are inflation-linked and a small proportion do not have a floor option which means they will be affected by deflation.
LV= says it will not be cutting income on its RPI-linked annuities and Axa also says deflation will not affect its customers.
Standard Life has 6,000 pensioners with an RPI-linked annuity without a floor and Pru has 9,000 clients in this position.
Standard head of pensions policy John Lawson says: “It would not be treating customers fairly to introduce a floor for customers who have not paid for it.”