HM Revenue and Customs (HMRC) says it expects as many as 70,000 people to notify it that they have tax to pay on offshore bank accounts.
The Revenue will soon have thousands more cases
The Revenue says there has been a last-minute rush of people telling them that they will be declaring unpaid tax.
HMRC launched its campaign earlier this year after discovering that 400,000 UK citizens have offshore bank accounts it did not know about.
The deadline for making a notification is midnight.
So far, 55,187 people have registered, telling the Revenue they will be paying the extra tax, plus interest, but taking advantage of the reduced 10% penalty charge on offer during the Revenue's campaign.
Of those, 6,675 came forward today, the last day for getting in touch.
The campaign got off to a slow start, but calls to the registration hotline have been coming in much faster in the past week.
At the Revenue's call centre in Dundee, 180 of the 700 staff there have been dedicated to answering requests for the HMRC's 44-page booklet spelling out what taxpayers have to do.
So far they have taken 34,000 phone calls there.
"We have been very busy indeed with 5,000 calls a day now," said Phyllis Lyske, the centre's manager.
"I think it has gone very well indeed, it was a bit slow to start with but it has picked up," she added.
Too much work?
People in the accountancy profession have suggested that the Revenue may have bitten off more than it can chew.
But an HMRC spokesman said it was well prepared.
"We think 100,000 of the 400,000 people need to talk to us to get on the straight and narrow," he said.
The department is not taking on extra staff as it feels it has enough to deal with the extra work, though the spokesman admitted this might take some time.
"It may take months, even years, but we have people ready to go," he said.
As well as dealing with people who confess they have failed to pay enough tax in the past, the Revenue will also have to chase up taxpayers with freshly-discovered offshore accounts who do not make any sort of confession.
Some will simply not have any extra tax to pay.
But others could find themselves in deep trouble.
"I think a lot of people have not paid tax on the principal sum paid into these accounts," said Ronnie Ludwig, of accountants Saffery Champness.
"There is a high likelihood that is what is holding them back."
He cited traders on eBay and people hiding business profits, as well as drug smugglers and money launderers.
Taxpayers can register for the Revenue's offer of reduced penalties by midnight tonight on the internet, or by 8.00pm on the special phone line.
But if someone finds they cannot get through the Revenue says it may well accept a slightly late registration if that person has a good excuse.
Once a notification has been made the full disclosure, plus the tax, must be made to HMRC by 26 November.