Susan Acland-Hood told the Public Accounts Committee that then Education Secretary Gavin Williamson instigated the event to thank his staff.
She said about two dozen people attended in the department’s canteen, where there were drinks and snacks.
She has now asked Cabinet Secretary Simon Case to investigate the issue.
Disciplinary action will be taken if he finds the rules aimed at stemming the spread of Covid, which were in place at the time, were broken.
Ms Acland-Hood told MPs on the committee that the event was a work-related gathering.
But she said on reflection it “would have been better” not to have held the event in that way at that time.
The event took place while London was under tier 2 restrictions which banned social mixing between households indoors.
And across England, meetings of groups of more than 30 were banned.
The event occurred less than a week before London moved into tier 3.
At the time, thousands of children were being sent home from school to isolate due to coming into contact with suspected coronavirus cases, thereby missing out on education.
And many head teachers were calling for their schools to be allowed to close early for Christmas because of high case numbers.
The confirmation of the event, first reported in the Daily Mail, comes just hours after the prime minister faced an angry barrage of questions in the House of Commons over an alleged party in Downing Street.