The 958,000 taxpayers who missed the deadline were equivalent to 8.18% of taxpayers required to make returns.
The penalties for late tax returns are an initial £100 fixed penalty which applies even if there is no tax to pay. Fines for non-return or non-payment then escalate.
The tax authority says the number filing online topped 10.4m for the first time.
About 11.7m taxpayers were required to file their 2018/19 tax returns by 11.59pm on 31 January.
About 11.1m managed to hit the deadline (more than 90%) and there were also 362,924 unsolicited or unexpected returns and late registrations (3.26%).
More than 700,000 submitted their tax returns on deadline day and the peak hour for filing was between 4pm to 4:59pm when 56,969 were filed.
Thousands filed their tax returns at the last minute with 26,562 completing their returns from 11pm to 11:59pm.
Angela MacDonald, HMRC’s director general for customer services, said: “It’s great to see that the majority of customers have submitted and paid their tax returns before 31 January.
“I’d like to thank everyone who filed and paid on time, but anyone yet to file or pay should contact HMRC straight away because we are here to help.”
HMRC says it will treat those with genuine excuses leniently but will focus penalties on those who persistently fail to complete their tax returns and deliberate tax evaders. Any excuse must be genuine and HMRC may ask for evidence.