Queues formed at the revenue's office in west London, which dealt with 300 visitors an hour before it closed at 3pm. Many of the country's 300 tax offices were similarly inundated with desperate inquiries.
Many callers were trying to avoid paying the pounds 100 fines for late returns.
But, with 1.8 million outstanding on Friday, it is likely that more than one million people will not have filed in time.
"We won't know how many tax returns we have had until Monday afternoon or Tuesday," said a revenue spokeswoman last night.
"Last year many returns were brought in in boxes by accountants on behalf of their clients, and the staff on duty over the weekend are there primarily to help people complete their returns."
The Inland Revenue said that it would accept no excuses for forms not returned by the time its staff start work this morning.
Returns that were pushed through office letter boxes throughout last night would be accepted. However, officials warned that not all centres had that facility.
Last year - the first time that taxpayers had to deal with self-assessment - it fined 820,000 people who failed to submit them on time. This year's total is likely to be higher.
Any taxpayer who is self-employed, on the higher-rate or has income from properties has to complete the self- assessment forms.
If the returns contain any missing or incomplete sections they can be rejected, and taxpayers could still face the penalty fine.
Late payers will rack up interest charges and those who still owe tax for last year - April 1997 to April 1988 - also have to pay in full, otherwise the revenue will start adding interest to the amount they owe, calculated by the day.Reuse content