It says 3.05 million workers want to work more hours each week, out of a total workforce of 29.41 million.
The number of workers in this position has shot up by 980,000 in the four years since the start of the economic recession in 2008.
The main reason for the growth of underemployment has been the economic downturn of the past few years.
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“During this period many workers moved from full-time to part-time roles and many of those returning to work after a period of unemployment could only find part-time jobs,” the statistical office said.
“Of the extra one million underemployed workers in 2012 compared with 2008, three-quarters were in part-time posts.”
The ONS said 1.9 million of the underemployed were in part-time jobs and this meant, in turn, that 24% of all part-timers wanted more work.
By contrast, only 5.5% of full-time staff said they wanted to work more hours.
Each quarter, as part of its Labour Force Survey (LFS), the ONS asks respondents a series of questions about their willingness and ability to work more hours.
Someone is counted as underemployed if they are working fewer hours than they would like.
