The Government, business groups and unions have welcomed another increase in the number of people in work, but worries continue on the pace of pay growth.
Employment rose by 137,000 in the quarter to May to 32.4 million, the highest since records began in 1971.
Unemployment fell by 12,000 to 1.41 million, giving a jobless rate of 4.2%, the joint lowest for more than 30 years, according to the Office for National Statistics.
Job vacancies nationally increased by 7,000 to 824,000 - the most since records began in 2001.
The claimant count, which includes people on Jobseeker's Allowance and the unemployment element of Universal Credit increased by 7,800 last month to 898,700, around 97,000 more than a year ago.
Locally the number of people claiming work related benefits such as Universal Credit remained largely the same as the previous month.
In the Blackpool North constituency, there were 1,635 people claiming, down 0.1 per cent on May. In Blackpool south there were 2,280, the same as the previous month, in Fylde there were 655 claimants down 0.1 per cent, Fleetwood and Lancaster had 1,200 claiming up 0.1 per cent, and Wyre and Preston North had 395, down 0.1 per cent.
In Preston, there were 2,010 people claiming, up 0.1 per cent on the previous month, in Chorley there were 1.095 people the same as last month.
Morecambe had 2,050 claimants up 0.6 per cent, South Ribble had 810, the same as last year, while the RIbble Valley had 550 people claiming, the same as the previous month.
Speaking about the national figures, Anna Leach, of the Confederation of British Industry, said: “The labour market continues to confound expectations of a slowdown, with the employment rate at another record high and the unemployment rate the lowest since the 1970s.
"But, despite high vacancies, pay growth has slipped to a six-month low, keeping up the pressure on people's living standards."
TUC general secretary Frances O'Grady said: "Wage growth has slowed again. Boosting pay packets should be a priority for the Government, but ministers are failing to act.
"We need to get the economy moving again. The Government should put the minimum wage up to £10 and give all public servants a proper pay rise."