Sutton Trust latest research on internships is covered by the BBC.
The government said HMRC already contacted employers who had advertised for unpaid internships to “ensure they are aware and compliant with the law”.
However, a fresh crackdown took place in the last three months.
It also said it would “formally ask” HMRC to focus activity in the coming year on firms which use unpaid interns, “through intelligence-led enforcement”.
“If this approach does not work, the government will review the existing policy and legal framework and will consider what other action can be taken”, it added.
Last month the Sutton Trust charity estimated that 40% of 70,000 internships undertaken annually were unpaid – but said young workers need a minimum of £1,019 per month to live in London and £827 in Manchester.
It backed cross-party calls to ban unpaid internships over a month long.