The campaign which began 9 July 2013 is aimed at people who have received a Self Assessment tax return or notice to complete a tax return for any year up to 2011-12 but have not taken action.
As part of the campaign, HMRC will be writing directly to several thousand people it has identified using intelligence-gathering software, and will follow up with calls to many of them.
HMRC are urging people to catch up on the best possible terms. They say that while some penalties will apply, it will cost the Taxpayer less if they come forward than if HMRC have to find them.
Those that identify themselves to HMRC have until 15 October 2013 to complete and submit the tax return and pay the tax and National Insurance Contributions.
After 15 October, if they have not submitted their returns and paid the tax due, penalties of up to 100 per cent of the tax, or even criminal investigation, could follow.