The gathering on 16 April 2021 was a leaving party for the former No 10 director of communications James Slack.
Prime Minister Boris Johnson did not attend the event and has so far not been issued with a fine.
The Metropolitan Police’s investigation of 12 events held across government began in January.
It was launched after an internal inquiry by senior civil servant Sue Gray passed information to the force.
Sources have confirmed to the BBC fixed penalty notices had been sent by email in recent days, as part of the first batch of 20 fines issued by police.
The BBC has seen the content of the emails. They say the police believe there are reasonable grounds that an offence was committed in contravention of Covid regulations.
The identity of recipients will not be revealed by the police unless they challenge the fine in court.
Two parties were held by Downing Street staff at No 10, the night before Prince Philip’s funeral. Mr Johnson was not at either of them, but has apologised.
One of the events was a leaving party for the PM’s then director of communications Mr Slack, who has also apologised.
Critics contrasted the behaviour of No 10 staff with pictures of the Queen sitting alone at her husband’s funeral, held under Covid restrictions.
Meanwhile, Monday’s Daily Telegraph claims the former director of ethics in the cabinet office, Helen MacNamara, was fined in connection with a leaving party the year before – in June 2020.
At various stages during the pandemic, the government imposed legally enforceable rules – including restrictions on social gatherings – to stop Covid from spreading.
The rules had been eased in England on 12 April 2021, but working from home continued to be recommended and socialising indoors with people from other households was not allowed. Meeting others outdoors was limited to groups of six people or two households.
The Met Police investigation, called Operation Hillman, is examining 12 gatherings on eight dates to see if Covid regulations were broken.
The prime minister is known to have attended at least three of the gatherings:
The police probe was launched after a separate inquiry was undertaken by senior civil servant Sue Gray.
In her separate, initial report, Ms Gray criticised “failures of leadership and judgement” over the gatherings, between May 2020 and April 2021.
An updated version of her report will be published in full, once the police have finished theirs, the prime minister has said.
Of the 16 gatherings listed in her initial findings, the police are looking at 12.
Labour leader Sir Keir Starmer has called for senior people who have been fined to be named.
On Sunday night, Conservative MP Steve Brine told the BBC there should be more transparency in the fines process.
He said it otherwise risked becoming a distraction from upcoming local elections, telling Radio 4’s Westminster Hour: “They should just be honest about who’s been tipped off with what and put it all out there and say, you know what, we got this wrong, or this person’s got this fine.”