The number of unemployed people, meanwhile, dropped by 8,000 in the three months to the end of July to reach 2.47 million, the Office for National Statistics said in a statement. The number of people in work also showed a record quarterly rise in the three months to July.
But the number of people claiming unemployment benefit unexpectedly rose in August for the first time since January.
The mixed report is unlikely to alter the view that Britain's recovery from recession is fragile and will be vulnerable to the deep public spending cuts due to be revealed next month.
The Office for National Statistics said the number of people claiming jobless benefit rose by 2,300 in August after a smaller than initially estimated fall of 1,000 in July. That was the first rise since January and confounded analysts' forecasts for a fall of 3,000.
The number of people without a job on the wider ILO measure fell by 8,000 in the three months to July to 2.467 million, the smallest fall since the three months to April. That left the jobless rate to 7.8%, as expected.
There was better news on the employment front with the number of people in work rising by 286,000 in the three months to July, the biggest quarterly rise since records began in 1971, although that was mainly due to a 166,000 rise in the number of part-time workers.
Average weekly earnings growth including bonuses rose at an annual rate of 1.5% in the three months to July, up from a 1.1% rise in the three months to June.