Employment rose to 32.3 million, the highest number since records began in 1971, according to the Office for National Statistics (ONS).
Unemployment fell by 46,000 to 1.42 million. The jobless rate stayed steady at 4.2%, the lowest since 1975.
Average growth in earnings, excluding bonuses, rose to 2.9% in the three months to March after a 2.8% rise in February. Inflation averaged 2.7% in the same period.
Senior ONS statistician Matt Hughes said: “With employment up again in the three months to March, the rate has hit a new record, with unemployment remaining at its lowest rate since 1975.
“The growth in employment is still being driven by UK nationals, with a slight drop over the past year in the number of foreign workers. It’s important to remember, though, that this isn’t a measure of migration.
“Growth in total pay remains in line with inflation, meaning real earnings are flat on the year.”
Commenting on the latest numbers, work and pensions secretary, Esther McVey, said: “Since 2010 we have seen 3.2 million more people move into work right across the UK. Youth unemployment has fallen by over 40% and the unemployment rate at its joint lowest since 1975
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“Today’s figures once again cement that turnaround, with an employment rate of 75.6%, and on average over 1,000 people each and every day, since 2010, getting a job.”
Ms McVey added: “With wages growing faster than inflation and increases in the personal tax allowance, not only are more people bringing home a pay packet but they are keeping more of their hard earned money for themselves and their families.”