According to the figures the number of people claiming Jobseekers Allowance in July fell by 3,800 to 1.46m.
Howard Archer of Global Insight said: "For now at least, unemployment continues to fall in reaction to the economy's ongoing growth since the fourth quarter of last year.
"However, it is notable that claimant count unemployment fell by a modest 3,800 while June's drop was trimmed to 15,900. This is well down down from the declines around 30,000 seen in May and April, and hints that the improvement in the labour market may be faltering."
Meanwhile average earnings rose 1.3pc in the year to June.