HMRC is pursuing investors in the Eclipse scheme, including celebrities, financiers and sports stars, for up to 20 times their original investment.
Courts ruled that the film investment partnership was in reality a tax avoidance scheme.
But an adviser to many of the investors said some of them now faced bankruptcy.
Nick Wood, a partner at Newport Tax Management, said: "There are a large number of people who have been left completely distraught.
"They have been given a three-month window to come up with what in some cases will be multiple millions of pounds."
The Eclipse partnership lost a Supreme Court appeal earlier this year over its use of tax breaks introduced by the government in 1997 to encourage investment in the film industry.
Now HMRC is demanding that investors repay their original investment many times over, because of the way the scheme was designed.
BBC business correspondent Joe Lynam said that to make a £1m investment, an Eclipse partner might contribute only £20,000 of their own money and borrow the rest.
"The tax relief on the whole amount would have been up to £400,000, or 20 times what they had risked. Here, HMRC may seek to recover the full £400,000," he said.
Labour MP Margaret Hodge, who chairs the all-party group on responsible taxation, said HMRC was right to pursue investors.
"If somebody cheats the benefit system, they have to pay the money back and are named and shamed. If somebody cheats the tax system, they should be treated in exactly the same way," she said.
Investors in a financing scheme aimed at helping the UK film industry are being asked to repay "multiple millions of pounds" following a court ruling.