Around 850,000 people face paying out £100 after failing to meet the tax return deadline.
HM Revenue & Customs (HMRC) said it will be sending penalty notices over the next fortnight, but added that 550,000 fewer people had failed to file their Self Assessment on time this year.
Those who continue to withhold their tax returns could see the size of their fine increase.
For example, anyone whose return is more than three months late will be charged an additional £10 penalty for each day it remains outstanding, up to a maximum of 90 days.
HMRC is giving people a small period of grace after strike action at its call centres on 31 January – originally the deadline for Self Assessment returns.
As a result, people who sent their 2010/11 return online on 1 or 2 February will not be penalised.
People who get a late-filing penalty can appeal against it if they think they have a reasonable excuse for not sending back their tax return in time, or they think a penalty should not have been issued for any other reason.
Reasonable excuses include illness or a family bereavement and appeals must be made in writing by 31 March.
And in a new initiative, HMRC has confirmed that anyone who receives a penalty, but who believes they don't need to be in Self Assessment, can call the department on 0845 900 0444.
If HMRC agrees, the return and the penalty will be cancelled.
"We want the returns, not the penalties. So anyone who still hasn't sent theirs should do so as soon as possible," HMRC's Stephen Banyard said.
"People who receive a penalty notice should act now to avoid further penalties. They should send in their return, appeal if they think they have a reasonable excuse, or contact us if they think they shouldn't have been in Self Assessment."
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