A report by IPPR suggests an oversupply of graduates means employers can persuade young people to work for free or in low-paid roles.
It says the number of leading graduate recruiters offering internships has grown by half since 2010 with many warning that securing a full-time job without such experience is unlikely.
Concerns have grown in recent years that unscrupulous employers are using unpaid internships to avoid employing paid staff.
Campaigners have also argued they reduce social mobility as only young people with financial support from their families can afford to take up unpaid roles.
Carys Roberts, a research fellow at IPPR, said: “There has been an unstoppable rise in internships since the last recession which shows no sign of slowing down.
“This is creating a structural bottleneck in the graduate labour market, at a time when fewer graduates are in high-skilled work than a decade ago.
“This means that young people are now more reliant than ever on finding a good internship to get a foot on the graduate jobs ladder.
“Although Theresa May agrees that getting on in today’s Britain is still ‘too often determined by wealth or circumstance’, internships are too often restricted to a privileged few.
For internships to help rather than hinder social mobility, universities, employers and government should act together to increase the overall availability of internships and minimise any barriers to take up for those who are disadvantaged.”
IPPR’s report recommends a “national opportunity programme” should offer residential internships for young people from disadvantaged backgrounds. It also calls for universities to broker work placements for students.
Former cabinet minister Alan Milburn, the chairman of the Social Mobility Commission, said: “This report is welcome. Internships are the new first rung on the professional ladder.
“They provide access to the best careers, but are too often unpaid and not advertised, making them inaccessible to young people who are locked out of these opportunities because they cannot afford to work for free.”