HM Revenue & Customs was last night expecting a late flurry of submissions from Britons keen to register their offshore bank accounts ahead of a midnight deadline.
But experts said the latest attempt to persuade tax dodgers to volunteer information about their overseas savings would net less than half the 45,000 people rounded up in the last disclosure campaign in 2007.
"My guess is that they won't get more than 20,000 registering," predicted Stephen Camm, a tax partner at accountant PricewaterhouseCoopers.
"That could leave still hundreds of thousands of UK people paying no tax on money kept in offshore accounts."
HMRC's last campaign to encourage people to declare money salted away in offshore bank accounts raised around £400m. But that is still a tiny proportion of the estimated annual £40bn cost of tax evasion.
"This is just the start of the Revenue campaign," warned Mr Camm. "It's been a cost-effective way for HMRC to collect taxes, but once they start costly investigations, they won't be so generous in discounting fines."
Anyone who registered by last night has until 12 March to pay tax owed on offshore savings. If they do so they only have to pay 10 per cent of the penalty charges. Anyone missing the March deadline will have to pay at least 20 per cent, and penalties will increase to 50-60 per cent after that, Mr Cann warned.
HMRC contacted 308 banks in its latest campaign, after targeting the UK's biggest eight banks in 2007. "We caught the majority of the bigger players last time," said a spokesman.
It is not illegal to have offshore accounts, but anyone who gets interest or income from overseas savings and investments must declare it on their tax return.