The details of 100 companies accused of illegally using unpaid interns have been passed to HM Revenue and Customs by business minister Jo Swinson.
Ms Swinson said the exploitation of interns was a "significant problem" and unpaid internships "attacked" the minimum wage.
The list, compiled by campaign group Intern Aware, is said to include some "big household names".
The minister said more needed to be done to enforce minimum wage law.
Unpaid internships have been criticised as barriers to social mobility and because they enable employers to avoid national minimum wage legislation.
Employers break the law if they employ unpaid interns in roles that are defined under law as "work".
This legal definition includes having set hours, being engaged for an extended period of time and being given a defined role rather than just observing.
Anyone who is "working" must be paid the national minimum wage - for anyone 21 or over it is currently £6.19 an hour.
Intern Aware, which campaigns in favour of paid internships, said the list covered a range of employers, from small to medium sized business to major companies.
The list covers sectors that are normally associated with internships, such as fashion, PR and the media, but also more unusual areas like accountancy, architecture and retail.
Some of the companies were advertising for internships that were clearly job functions, like "administrative internships", the group said.
Luxury London department store Harrods was recently forced to pay an intern £1,800 for work carried out in its marketing department after "misclassifying" her as a volunteer.
Ms Swinson told the BBC she had been "only too happy" to pass the letter on to HMRC, adding that it was "right" that inspectors should investigate it.
"We have national minimum wage laws and they are there for a reason. If these are being flouted, then that needs to be dealt with," she said.
"There is a significant problem in society where people are being exploited for no money when they should be being paid.
"We have got to change attitudes and make sure companies realise it is not appropriate. Where there is a job that needs doing, then it needs to be treated as a job and not be done be someone who is not being paid. This attacks the national minimum wage.
'Only the start'
"Across many sectors, like fashion and the media, this has very much been the generally accepted way of doing things. It is a cultural thing and that needs to change.
"We need to make sure we enforce the law and increase awareness of the problem."
However, Ms Swinson stopped short of backing new legislation in the area to make the rules tighter.
She said HMRC was already making progress in enforcing the law, last year bringing in £4m of wages arrears for 26,500 individuals who were either underpaid or paid no wage at all. This was up from £3.6m in the previous year.
She said the government was also looking at ways to "name and shame" companies which haven't properly complied with the law.
"This is an issue about social mobility as much as anything else. It shouldn't be that only those who can afford it should be able to have those opportunities. It is not helpful if they are only accessible to the rich," she added.
Following criticism last year, the Liberal Democrats changed their internship programme so it now pays the minimum wage, although some Lib Dem MPs, and MPs from other parties, still advertise internships which pay expenses only.
Intern Aware's co-director Ben Lyons said he was pleased Ms Swinson had decided to pass the list of employers on to HMRC. He said: "This is only the start and a lot more needs to be done."
A spokesman for HMRC said it did not comment on individual investigations.