Unemployment among 16-to 24-year-olds also dropped, to 935,000, but the jobless rate for young people, at 20%, remains worrying.
The number of women claimants increased by 9,300 to reach 474,400, the highest figure since October 1996. This is the tenth consecutive rise in the number of women claimants.
The total number of people claiming Jobseeker's Allowance rose by 12,400 in April to 1.47 million. During the period, the number of people in employment rose by 118,000, reaching a total of 29.24 million in employment in the UK.
There were 469,000 job vacancies in the three months to April 2011, down 30,000 from the three months to January 2011, but up 3,000 from a year earlier. The estimates include vacancies for temporary jobs in connection with the 2011 Census.
Excluding the Census vacancies, there were 461,000 job vacancies in the three months to April 2011, down 4,000 from the three months to January 2011 and down 5,000 from a year earlier.
In the three months to March 2011, 123,000 people had become redundant, down 24,000 from the three months to December 2010 and down 53,000 from a year earlier. The redundancy rate was 4.9 per 1,000 employees, down 1.0 from the previous quarter and down 2.2 from a year earlier.
Total pay (including bonuses) rose by 2.3% on a year earlier and regular pay (excluding bonuses) rose by 2.1% from March 2010.
Steven Kirkpatrick, managing director at recruitment firm Adecco, said: “A second consecutive increase in employment figures provides jobseekers with some hope. However, reports suggest that the number of advertised vacancies is decreasing in many sectors, representing a continued caution among employers, who are still unable or unwilling to create new permanent positions in an unstable climate.
"Key growth areas such as banking, finance and insurance are seeing an uplift in the creation of new job vacancies, but for the jobs market to really show signs of recovery we need to see the creation of new roles extended across other large industry sectors, such as engineering and manufacturing and retail.”
Tom Lovell, group managing director of recruitment consultancy Reed, added: "Now the cluster of bank holidays is out of the way, we expect to see an increase in job opportunities as organisations look to fill any gaps before the summer holiday season gets into full swing.
“April did see an upturn in the temporary jobs market, with Reed seeing a 9% year-on-year increase in the number of temporary workers placed in April 2011 compared to April 2010.
“We have also seen some sectors perform particularly well in April, with the number of interviews arranged in technology, hospitality and education sectors all up on the same period last year.
“Following the overall strong increase in job vacancies during the first quarter of this year, the Reed Job Index also found that there were 22% more job opportunities available in April this year than April 2010, with growth coming from the private sector. This is reflected in the falling unemployment and rising GDP figures for the same period.”