The number of people in work also reached a record high of 32.2 million, according to new figures
Employment increased by 55,000 in the quarter to February, the highest figure since records began in 1971, giving a record rate of 75.4%.
Unemployment fell by 16,000 to 1.42 million, the lowest in more than a decade, giving a jobless rate of 4.2%, the lowest since 1975, according to the Office for National Statistics.
Average earnings increased by 2.8 per cent in the year to February, unchanged on the previous month and the highest since September 2015.
The latest CPI inflation figure is 2.7% and is expected to remain unchanged when new figures are published on Wednesday.
Matt Hughes, senior ONS statistician, said: “The labour market continues to be strong and, for the first time in almost a year, earnings have grown slightly after inflation has been taken into account.”
The number of people classed as economically inactive, including students, those on long-term sick leave, on early retirement, or who have given up looking for work, fell by 2,000 to 8.7 million in the latest quarter, giving a rate of 21%, a joint record low.
The claimant count, which includes people on Jobseeker’s Allowance and the unemployment element of Universal Credit, increased by 11,600 last month to 855,300, the highest for more than three years.
Job vacancies remained unchanged at 815,000, while the number of self-employed workers fell for the second successive quarter – down by 18,000 to 4.76 million.