A Revenue spokesman said this year it was expecting 90% of returns to meet the deadline.
This would equate to around 970,000 returns missing the 31 January deadline, although it is unclear whether all these taxpayers would face a £100 fine.
This comes despite a relaxation in its rules giving taxpayers an effective one-day extension to the January 31 deadline for avoiding the penalty.
Assuming the 90% is achieved, the number of late or missing returns would be up more than a quarter of a million on last year. In each of the first two years of self-assessment, some 650,000 returns were late.
Additional measures were taken this year in an attempt to ease the late rush. Tax payments could be made at post offices and tax offices as late as Monday and Revenue offices opened over the weekend to take returns. Enquiry centres also accepted payments of tax.
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