Youth unemployment was down by 17,000 to 1.02 million. But the number of people unemployed for more than a year increased by 27,000 to 887,000, the worst total since 1996.
The number of people claiming Jobseeker's Allowance fell by 13,700 to 1.59 million in April.
Part-time working hit another record. The ONS said the total number was 7.99 million between January and March, up 118,000 compared with the previous three month period between October and December.
Those working part-time because they couldn't find a full-time job was also the highest since records began in 1992 at 1.42 million, up 73,000 on the previous quarter.
Of the 45,000 drop in unemployment, 42,000 were men and just 3,000 were women.
"It's still women and young people who are bearing the brunt of the recession," said the Unison union general secretary Dave Prentis.
I don't have enough work to fully pay my rent and support myself. It's a combination of benefits and friends until I hit a good patch where I can pay a few things off
Employment Minister Chris Grayling said overall the figures were a "welcome step in the right direction".
"For a number of months now, employment has been growing and this is starting to feed through into improving unemployment figures.
"However, we still face significant international uncertainty so we need to hold firm on our current economic strategy and continue to do everything we can to ensure unemployment continues to fall."
Bank of England governor Sir Mervyn King also said that the latest figures were consistent with a gradual recovery in the UK economy, while pointing to the huge risk to the UK economy posed by the crisis in the eurozone, the UK's biggest trading partner.
Shadow work and pensions secretary Liam Byrne said it was "really worrying to see the soaring long term costs as the number of long term unemployed surges towards the 1 million mark - the highest since the Tories were in Government last time".
