The Office for National Statistics (ONS) says 31% of graduates are overeducated for the job they are doing.
For those graduating before 1992, the number was only 22%, but this jumped to 34% for those graduating after 2007.
London had the highest proportion of overeducated workers in the UK, with about 25% overqualified for their job.
Graduates in arts and humanities were more likely to be under-using their education.
"We note that the incidence of overeducation does seem higher for certain age groups," and in particular for those aged 25 to 49 years, it said.
"The relatively high incidence of overeducation for the 35 to 49 years age group indicates that overeducation is a persistent phenomenon in the UK labour market," it said.
The overeducation rate for all workers of about 16% for 2017 is largely unchanged since 2006.
And, while it says it can not be sure, the ONS says priorities for some people over-and-above money may contribute to their below-par post-graduation earnings. This, it says, may account for the unchanging rate of overeducation.
The ONS said it assumed education was a measure of ability and did not distinguish it from skill. It also said it assumed wages as its measure of productivity, meaning the research does not show whether overeducation has an effect on output per worker.
What does overeducation mean?
"A person can be overeducated if they possess more education than required for the job," the ONS says.
But it also uses the term to mean when a worker's skills and knowledge are not being used.
"It can also be seen as a form of underemployment, hence contributing to the extent of labour market slack," the national stats gatherer says.
However, a degree still attracts higher earnings, according to government data from earlier this month. And two degrees will yield even more.
Graduate earnings figures show that up to the age of 30, postgraduates typically earn £9,000, or about 40%, more than those without degrees.
This is double the £4,500 per year gap - about 21% - between those with an undergraduate degree and non-graduates.
Case study: Elizabeth
Elizabeth graduated recently from the University of Manchester with a degree in chemical engineering. She has not been able to find a degree-level job and has worked a succession of minimum wage jobs.
"I'm sad to have become one of those statistics of female graduates who never become engineers, and dread the next 50 years in minimum wage jobs, because I have no way of getting out of the situation. I should have realised people don't want to employ women in that field," she said.
"I regret my choice of degree every day. I could have been doing anything by now. People ask me why I am a kitchen porter when I can speak languages and have a degree. It's sad that people who are less qualified are much further on in their career than me.
"A lack of a driving licence seems to have proved a huge hindrance to my progression, and in many ways might have been more useful than the degree."