The revenue said the 600 notices it has sent out have already resolved over £25m worth of payments, despite recipients having 90 days to pay back contentious tax.
It added that many taxpayers are choosing to contact them directly about settling their outstanding affairs rather than waiting to receive a notice.
David Gauke, financial secretary to the treasury said: “Accelerated payments are changing the economics of avoidance by removing the cash-flow advantage that avoidance scheme users have had until now.
“It is only fair that those who use avoidance schemes should have to pay their tax upfront, like the vast majority of other taxpayers who don’t try to shirk their responsibilities.”
Jennie Granger, director general of enforcement and compliance at HMRC said anyone concerned about being able to pay a notice should contact the government body “as soon as possible to discuss their options”.
Accelerated payment notices are issued when a taxpayer has entered into a tax avoidance arrangement that has been notified to HMRC under the disclosure of tax avoidance scheme rules. HMRC were granted Royal Assent to issue the notices in July.
The revenue issued its first accelerated payment notices at the end of August, and aims to eventually send 2,500 a month until it has sent out a total of over 40,000.
The notices are expected to cover £7.1bn in disputed tax, with 33,000 going to individuals and 10,000 to businesses.