Beginning today (9 July), the campaign 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.

Marian Wilson, HMRC’s head of campaigns, said: “This is definitely the best time to catch up, on the best possible terms. While some penalties will apply, it is likely to cost people more if we have to find them rather than them coming to us. We have made it easy to take part.

“We know this approach works because Campaigns launched so far have produced more than £547m by people coming forward voluntarily. And evidence shows that people who change their behaviour voluntarily are more likely to remain compliant longer. We will continue to analyse information using Connect, our state-of-the-art risking engine, and will be looking more closely at people who have gaps in their tax records.”

The campaign follows last year’s Tax Return Initiative campaign, which covered higher-rate taxpayers who had failed to submit 2008-09 or 2009-10 returns.

Under that campaign, more than £30m was paid when over 3,000 people came forward voluntarily, filing more than 5,500 tax returns.

Once participants have told HMRC that they want to take part in the campaign, they have until 15 October 2013 to complete and submit a tax return, and pay the tax and National Insurance Contributions (NICs) that they owe.

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.