Official figures show that the number of people claiming jobless benefit in the UK rose by 20,800 in September. This was less than expected and was the smallest rise since May 2008.
The Office for National Statistics said that took the claimant count rate to 5% from 4.9% August, its highest since September 1997.
The number of people without a job on the wider ILO measure of unemployment rose by 88,000 to 2.469 million in the three months to August, leaving the jobless rate at 7.9% and below expectations for a reading of 8%.
The figures show that while unemployment is still rising in Britain, the rates of monthly increase are easing, in a sign that the labour market may not be as hard hit by recession as some had feared.
The economy is starting to show signs of recovery after a year-long recession and predictions from some analysts that unemployment rates could top 10% next year.
There is still a great deal of uncertainty about the strength of any recovery, given a continued dearth of bank lending despite extensive measures from the Bank of England and government to get credit flowing again.