The number of people claiming unemployment benefit fell by 5,200 to 1.28 million - the lowest level since June 1980. The number in work rose to a record 27.36 million.
Earnings growth eased to 4.3 per cent in May from 4.6 per cent in April - below the Bank's "tolerance threshold" of 4.5 per cent and the lowest since September 1997. However, real wage rises, excluding inflation, have soared from 1.7 per cent in December to 3 per cent in May.
Andrew Smith, the Employment Minister, hailed the figures as a "considerable achievement".
"There is continuing job generation without inflationary pressure. The UK's employment rate is second only to Denmark in the whole of the European Union," Mr Smith said. He welcomed the fall in earnings growth but warned that continued wage restraint was essential.
"Wage moderation is a key requisite for sustainable growth and job generation," he said.
Economists said the figures had postponed the need for interest rate rises. "Although the labour market remains tight and GDP growth is set to pick up strongly over the next year, any tightening in monetary policy remains some way off," said Richard Iley of ABN Amro.
The figures showed a twin-speed economy - both between services and industry and between North and South.
Manufacturing industry lost 153,000 jobs in the three months to May - a fall of 3.7 per cent - while the services sector workforce grew 1.5 per cent year-on-year.
Unemployment rose in the North-east, West Midlands, Wales, East Midlands and the South-west, according to Labour Force Survey data.
There were falls in eastern England, the South-east, London, Yorkshire and the North- west.