Claims for unemployment-related benefit fell in most parts of Suffolk and north Essex last month, according to official figures.

But there were signs nationally that the jobs market may be cooling, despite total unemployment falling to a six-year low.

Figures from the Office for National Statistics (ONS) show that a total of 1.6m people were out of work in the quarter to September, a fall of 37,000 compared with the previous three months.

However, the narrower count of those eligible to claim the Jobseeker’s Allowance increased on a seasonally adjusted basis by 9,800 in September to 803,300 – the third consecutive monthly rise.

The number of people in work now stands at a near-record high of just under 32m while the employment rate of 74.5% is the highest since records began in 1971.

ONS statistician David Freeman said: “Unemployment is at its lowest for more than 10 years and the employment rate remains at a record high. Nonetheless, there are signs that the labour market might be cooling, with employment growth slowing.”

On an unadjusted basis the claimant count fell by around 18,000 to 518,064 and most parts of Suffolk and north Essex followed this trend.

The local jobless rate eased by 0.1 of a percentage point in Forest Heath, where the count fell by 21 to 164 (a rate of 0.4%), Mid Suffolk, down 20 to 305 (0.5%), St Edmundsbury, down 15 to 434 (0.6%), Suffolk Coastal, down 32 to 295 (0.4%), and Waveney, down 57 to 485 (0.7%).

Smaller falls, relative to the size of the local workforce, saw the rates remain unchanged in Babergh, down 30 to 299 (0.6%), and Ipswich, down 43 to 1,349 (1.6%).

The picture was more mixed in north and mid Essex where the count increased in Colchester, by 22 to 1,060, and Uttlesford, by 20 to 205, although the jobless rates remained unchanged at 0.9% and 0.4% respectively.

Tending saw the largest fall, with the count down by 64 at 1,353 and the rate by 0.1 at 1.8%. Smaller falls left the rates unchanged in Braintree, down 45 to 717 (0.8%), Chelmsford, down 27 to 817 (0.8%), and Maldon, down 18 to 208 (0.6%).