The taxman should explain to those failing to pay tax how they might evade prosecution if they own up, says a group of MPs on the Commons Treasury Committee.
The MPs are also worried a deal struck between the UK and Swiss governments might actually encourage more people to conduct their financial affairs offshore.
In a report which concludes the government will never accurately know how much tax goes unpaid to the Treasury, MPs say that while "egregious" tax evaders should always be prosecuted, it should be made clear that many will not, if they come forward and own up.
They write "It is important that those outside the tax system who wish to become compliant are not deterred from doing so by an unfounded fear that they may be prosecuted. HM Revenue and Customs (HMRC) should publish on its websites case studies of taxpayers who have not been compliant in the past but who have approached HMRC to settle the tax they owe.
"These should make clear that in the vast majority of cases the taxpayer’s disclosure did not result in prosecution and should be understandable to the lay reader."
The MPs were told that the number of successful prosecutions by HMRC had fallen by 40% since 2007. The most recent figures - for 2008–09 - showed only about 150 each year. HMRC said it was now targeting highly organised and criminal tax evasion cases.
The MPs heard that most people who decided to come forward and settle their unpaid tax did so voluntarily, often because they had had a child or got married, rather than because of any campaign waged by the government.
HMRC spends around £8bn a year in legal costs recouping unpaid tax but the MPs believe a new approach is needed.
They say: "By far the most efficient way of closing the tax gap is encouraging voluntary compliance. A process whereby taxpayers and HMRC work together to ensure that taxpayers voluntarily pay the correct amount of tax, sometimes
following negotiation and agreement, is far less costly than the alternative."
The report also looks at a deal signed by George Osborne in November 2001 - the UK-Swiss Confederation Taxation Cooperation. It means the Swiss government will impose a levy on UK taxpayers banking in Switzerland. This was hailed as a breakthrough in curbing offshore tax avoidance by Osborne, but the MPs say: "The rates of tax to be withheld from income and capital are lower than the top rates of tax in the UK. This seems to reward those who have deliberately avoided tax over those who have not."
The Public and Commercial Services (PCS) union said the MPs' report missed the point. PCS general secretary Mark Serwotka said: "The main barrier to tackling the tens of billions of pounds lost to our public finances every year is the loss of tens of thousands of HMRC staff.
"It makes no economic sense to be cutting the very people capable of addressing the problem of uncollected tax, but this confused report by the Treasury select committee appears to have missed this rather obvious point."