Millen, who created the high street brand 35 years ago, claimed she had been the victim of fraud by the collapsed Icelandic bank Kaupthing, The Times reported.
The bank financed the buyer who bought her business in 2004 for £95m, it added.
The fashion designer said that in 2001 her accountants advised her to enter into a tax avoidance scheme named Round the World.
HMRC disputed the scheme in 2010 and issued Millen with a notice to pay £6m in September last year.
However, she told the newspaper that her battles with Kaupthing “have led to my inability to pay HMRC”. She said she was “deeply devastated” after declaring bankruptcy in the High Court on Tuesday.
The Round the World scheme claimed people could avoid up to £70m in capital gains tax on the sale of shares, by transferring the shares to trustees in Mauritius. However the Court of Appeal later ruled that the scheme was taxable in the UK.
An HMRC spokesperson said the Revenue does not comment on the tax affairs of individual taxpayers.
It added, “Our aim is to efficiently collect monies and debts due, using the range of powers available to us.
"Anyone who anticipates payment problems should call us and we will do all we can to help, including offering time to pay. We have an outstanding track record for supporting those with genuine problems."
The Kaupthing bank, which was Iceland’s largest, collapsed in October 2008 with debts of $50bn (£40bn).
The Serious Fraud Office (SFO) opened an investigation into suspected fraud offences committed within the UK jurisdiction in relation to the bank in December 2009, but then dropped it in October 2012 claiming that there was insufficient evidence to justify continuing the inquiry.