HM Customs and Revenue (HMRC) has published a list of more than 800 schemes that it believes are deliberately designed to avoid tax.
The list consists of a series of numbers, allowing them to be identified by the tax-payers involved.
As soon as it receives new legal powers in August, HMRC will be demanding the disputed tax as "accelerated" payments.
Accountants warned that the number of individual bankruptcies could go up as a result.
Celebrities including David Beckham and singer Katie Melua are among those who have been members of such schemes.
In total, it is thought around 33,000 people will receive tax demands for billions of pounds from HMRC over the next two years.
They will be given 90 days to pay, and they will only get the money back if a court eventually decides in their favour.
HMRC said it was only giving a list of numbers - known as Scheme Reference Numbers (SRNs) - as the promoters of tax avoidance schemes do not have to publish their names.
But those filling out a tax return do have to put the number on the form, so they will be able to identify if they are likely to be asked for a payment.
Accountancy firms said that, in the case of many schemes, it would prove extremely difficult for taxpayers to challenge a request for payment by HMRC.
One firm also warned that some people will not have enough money to pay, especially since interest payments will have mounted up over the years.
"Individuals and businesses will be expected to raise external finance to pay the tax, or sell assets," said Dawn Register at accountants BDO.
"This could lead to many businesses facing a major cash flow problem, and equally individual bankruptcies could increase," she said.
Most of the schemes given recent publicity, including Icebreaker and Ingenious Media, involve investors putting money into business ventures that make losses.
Examples include investments in the film and music industries.
Those losses can be offset against income, so reducing liability for tax. But such schemes remain perfectly legal.
Last week the singer Katie Melua admitted she had been "clueless about tax" when she signed up to one such scheme, known as Liberty, nearly 10 years ago.
But she said she had now paid all of the tax that she owed at the time.