The Association of British Insurers said the market was still worth £11.9 billion, but a growing number of retirees are choosing to defer converting their pension pot into income, using solutions such as drawdown.
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Leading broker Hargreaves Lansdown has reported a 40 % increase in demand for drawdown business in 2013.
Tom McPhail, head of pensions research at Hargreaves Lansdown, said: "The retirement income market appears to be shifting, with demand for annuities collapsing and surging interest in drawdown.
Last week the Financial Conduct Authority published a review which confirmed that condemned around 130,000 people each year, or eight out of 10 who stick with their insurer for their annuity, could be getting a better retirement income by shopping around.
But the review was widely criticised for acting too slowly to prevent retirees missing out, and to stop hidden commissions and unsuitable sales from broking websites.
The ABI figures showed that enhanced (medically underwritten) annuities for people with poorer health took for 28% of sales in the last quarter of 2013. That is double the 14% share in 2010, which critics say shows the need for compulsory suitability checks.