Unemployment and jobseeker's allowance claimants have both fallen, but the number of over-65s in a job has reached a record one million.
Unions said that with almost a million young people out of work, it is clear there are not enough jobs, while experts believe people are working longer to top up inadequate pensions.
The Prime Minister said the Government had a "good record" on jobs, as the figures also revealed that unemployment fell by 5,000 to 2.5 million and the numbers claiming jobseeker's allowance shrank by 8,600 last month to 1.5 million. A record 29.7 million people are in work after a rise of 24,000 in recent months.
The Office for National Statistics (ONS) data showed that over 65-year-olds in work has topped a million for the first time since records began in 1971. Almost one in 10 people in the age group are working - 615,000 men and 388,000 women.
Institute for Employment Studies director of research Jim Hillage said: "While this reflects a welcome willingness among employers to recruit and retain experienced people, it may also reflect the need that some older people have to top up inadequate pension arrangements."
Other data disclosed that public sector employment has fallen by 22,000 to just under 5.7 million. the lowest figure since 2001. Ministers pointed to a growth in jobs in the private sector, up by 46,000 to 24 million in recent months.
The UK's employment rate is now 71.5%, while 7.8% of the population is jobless, with 22% classed as economically inactive, including students, those on long term sick leave or who have given up looking for work.
The so-called claimant count has fallen for seven months in a row and has dipped to its lowest total since May 2011. The fall in unemployment in the quarter to April was entirely due to men finding work, while the number of women out of a job rose by 7,000 to 1.09 million.
TUC general secretary Frances O'Grady said: "Today's figures show that any economic green shoots are confined to the stock market and the pay of top bosses.
"While there is a record number of people in work - due to a rising population and people working past state pension age - the chances of actually being in work has fallen in the last three months."