Tax dodgers should be "named and shamed" to stop celebrities using legal loopholes to cut the amount they pay to the Treasury.
The Public Accounts Committee says promoters of tax avoidance schemes are "running rings" around the taxman by taking advantage of the time it takes HM Revenue and Customs (HMRC) to shut them down.
It wants promoters and those who use their schemes to be listed and called on HMRC to be "more robust in its approach".
Margaret Hodge, who chairs the Public Accounts Committee, said: "We have seen how public anger and consumer pressure can influence large companies, such as Starbucks, to behave more responsibly.
"HMRC should publicly name and shame those who sell or use tax avoidance schemes in order to discourage such activity.
"With at least £5 billion lost to tax avoidance each year, HMRC has got to get much more robust in its approach."
Mrs Hodge highlighted the case of comedian Jimmy Carr, who last year admitted making a "terrible error of judgment" after using a complex avoidance scheme to reduce his tax bill.
The K2 scheme he used enabled its members to pay income tax rates as low as 1%.
"Promoters of 'boutique' tax avoidance schemes like the one brought to our attention by the case of Jimmy Carr, are running rings around HMRC," Mrs Hodge said.
"They create schemes which exploit loopholes in legislation or abuse available tax reliefs such as those intended to encourage investment in British films, and then sign up as many clients as possible, knowing that it will take time for HMRC to change the law and shut the scheme down.
"Their clients can then take advantage of this window of opportunity to make a lot of money at the expense of the UK taxpayer, while the promoter simply moves on to a new scheme and repeats the process.
"It is a game of cat and mouse and HMRC is losing."
According to the Public Accounts Committee, some tax avoidance schemes have been shut down because of tax rules that require promoters to notify HMRC of new tactics.
However, it warned officials do not know how many promoters are ignoring the requirement.
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