Tax dodgers are being pursued at "unacceptably slow" levels by HM Revenue and Customs, putting millions of pounds due for Treasury coffers at risk, according to a critical report by MPs.
The agency has also overstated the success of its attempts to crackdown on the practise because its targets were set to low, the Public Accounts Committee found.
Delays in dealing with the controversial Liberty scheme - which created a tax loss for investors that they could offset against other income - used by celebrities, doctors and judges mean the case has only been taken to a tribunal this year despite being shut down in 2009.
MPs warned that up £10 million of the total £400 million tax at stake may not be recoverable because HMRC failed to start inquiries into 30 cases within the legal deadline.
"This may be just the tip of the iceberg," Mrs Hodge said. "Although HMRC says Liberty was an exceptional case among the 750,000 personal tax return inquiries each year, it was unable to tell us how much delays had cost across the different tax avoidance schemes."
Around 2,000 people are believed to have used the scheme, including singer Katie Melua, who paid her taxes in full after learning she was among a number of stars who had invested in it.
The PAC said action against tax avoiders "continues to be unacceptably slow, putting tax revenues at risk".
It raised concerns about HMRC's slow progress acting on information from the Falciani list, which identified 3,600 Britons potentially avoiding tax using the Geneva branch of HSBC.
The committee found that the agency had received £135 million from individuals on the list, compared to £220 million received by Spain and £188 million received by France.
Mrs Hodge added: " HMRC says delays in recovering the tax withheld by those participating in tax avoidance schemes are partly due to delaying tactics by scheme promoters.
"HMRC must do more, faster. It should report on the progress it has achieved by using new powers granted by Parliament to tackle tax avoidance and show that it is using its existing powers with sufficient urgency.
"HMRC does not do enough to tackle companies which exploit international tax structures to minimise UK tax liabilities.
"Recent changes to the UK tax regime, such as those for controlled foreign companies, have been challenged by international bodies like the OECD and European Commission as constituting 'harmful tax practices.'
"These changes, including the introduction of the patent box relief, make it easier for global companies to avoid paying tax in the jurisdictions where they make a profit.
"Some international tax experts believe that the UK's tests for companies to gain tax residency are less rigorous than in other EU jurisdictions. Research into seven companies who have recently relocated to the UK for tax purposes showed very little inward investment was generated or jobs created in the UK in return for the tax benefits the companies receive."
HMRC also presented "misleading information" to Parliament about its improvements in collecting cash from tax avoidance, evasion and crime after a £1.9 billion error in the way its targets were set and the blunder went under undetected for three years, the committee said.
Mrs Hodge said: "It is amazing that HMRC made a £1.9 billion error when it established its baseline and set targets for its compliance work.
"This means HMRC has been overstating the extent to which its performance on compliance yield has improved over the 2010 spending review period, and it inadvertently presented misleading information to Parliament about the improvement in its performance.
"Astonishingly, this significant error in a key performance measure went undetected by HMRC's own system of governance and internal audit for three years.
"HMRC should make sure the governance arrangements around its performance are sufficiently robust. It should be more transparent about its compliance yield estimates and maintain a comparable measure of compliance yield over time so we are not comparing apples and pears."
A HMRC spokesman said: "We have accelerated collection of tax from avoiders enormously - since the Government introduced accelerated payments avoiders have already agreed to pay well over £25 million.
"By 2016 we expect to have issued accelerated payment notices to around 43,000 avoidance users covering over £7 billion and we are also using new legislation enabling us to ask the tax courts to designate certain avoidance promoters as high risk, with accompanying fines of up to £1 million.
"The committee recognises we have addressed their key comments about tax avoidance. The way we now work makes it clear to promoters and users of schemes that we will robustly tackle tax avoidance wherever it happens so increasingly taxpayers are contacting us to help disentangle them from schemes that simply don't work.
"We are also effectively challenging multi-nationals whilst bringing in the colossal sum of £31 billion from large business since 2010 alone.
"We will work closely with the National Audit Office to ensure there is no repeat of the base line error for which we apologised to the committee.
"However, even taking this into account we exceeded our targets for tackling tax dodgers and criminal gangs every year since 2010."
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