The government has referred 100 companies for investigation by HM Revenue and Customs after a campaign group told ministers they might be breaking the law through their use of unpaid interns.

The firms, which have not been identified publicly but are understood to include a number of household names, were referred by Jo Swinson, the junior employment minister, after a meeting she had with Intern Aware, which campaigns against the abuse of the internship process.

While companies are free to offer work experience, where this ends up amounting to a job – for example if hours and duties are set and the position lasts for a long time – companies are breaking employment laws if they do not pay at least the minimum wage.

Aside from the illegality, critics say the use of long-term, unpaid positions as an entry point to popular professions in effect excludes those without well-off parents or other means to support themselves.

Abuse of the process remains rife, said Ben Lyons of Intern Aware. The group was able to compile its list of suspect companies simply by trawling jobs websites or searching online for "unpaid internship".

It sought the meeting with Swinson to reveal to her the scale of the problem, Lyons said. "Just to demonstrate the problem, we sent her these 100 ads, most of which were taken from large job sites and would seem to be the tip of the iceberg. We were disappointed HMRC haven't seemed to be recognising what a big issue this is."

Lyons said he co-founded Intern Aware as a way of tackling inequality. "We set it up at university because we were angry at seeing friends of ours, who were bright and hardworking, being priced out of professions because they couldn't afford to work for free. It's not just that they're wrong, but lots of these companies are breaking the law."

Commenting on the referral, Swinson said: "The law on the national minimum wage is clear. If somebody on a work experience placement or internship is a worker under NMW (national minimum wage) legislation, then they are entitled to the minimum wage."