Unemployment fell by 121,000 to 2.12 million between March and May, official figures showed.
The number of people claiming jobseeker's allowance last month fell by 36,300 to 1.04 million, said the Office for National Statistics.
Average earnings increased by 0.3% in the year to May, 0.5% down on the previous month.
More top news
Yorkshire Water says the tap water in Thorne, near Doncaster, is still not fit to drink after a contamination scare.
In December 2012, gunman Adam Lanza shot dead 20 children and six teachers in the Connecticut school, before turning the gun on himself.
The study, conducted by the European Banking Authority, looked at how much capital would be used up in adverse economic conditions.