The prime minister's father, Stanley Johnson, has been pictured shopping without a face covering, breaking current Covid-19 restrictions.
Mr Johnson - a former Tory MEP - has apologised, claiming he may not be "100% up to speed" with current rules after returning from abroad.
Fines for not wearing a covering in a shop were raised by the government last week to £200 for first time offenders.
Former Labour leader Jeremy Corbyn has also apologised for breaking the rules.
He was pictured at a dinner party which appeared to have nine guests, going against the government's "rule of six".
Asked about the pictures, Boris Johnson's official spokesman said it was now for the police to "determine what action to take", adding: "What the prime minister is clear on is that the rules apply for everyone and everyone should follow them".
The PM's father was seen in a newsagents in West London without a mask on Tuesday, with the picture first appearing in the Daily Mirror.
It came a day before his son, Boris Johnson, held a press conference, appealing to the public to "follow the rules" and warning fines would be imposed on those who don't.
Speaking to the Mirror, Stanley Johnson said: "I'm extremely sorry for the slip up and I would urge absolutely everybody to do everything they can to make sure they do follow the rules about masks and social distancing.
"The fact this was my first day back in the UK after three weeks abroad is, I am sure, no excuse for not knowing the rules."
A Downing Street spokesman said the PM's father "fully understands that it is vital for everyone to abide by the rules".
Mr Johnson was criticised back in July for travelling to Greece during the coronavirus lockdown.
The guidance on air travel from the UK Foreign Office advised against "all but essential international travel" at the time and insisted on a two-week quarantine on return.
But he told the Daily Mail he was in the country "on essential business" to ensure a property he rents out was "Covid-proof" before holidays restart.
The picture of Mr Corbyn appeared in the Sun, with the newspaper saying the gathering had taken place on Saturday.
Across England, people face fines starting at £200 for meeting inside or outside in groups of more than six - although the rules are stricter in some parts of the country.
The North London MP told the paper: "I recently had dinner at a friend's house where the number of guests eventually exceeded five.
"I understand that remaining at the dinner was a breach of the rule of six. I apologise for my mistake."
Responding to the picture, Labour leader Sir Keir Starmer said: "All of us should obey the rules, Jeremy knows that, I know that, all of us have to comply with the rules.
"I have said throughout that whatever the Government rules are, we should all follow them. We have got a duty to so."
Asked whether Mr Corbyn should be fined, Sir Keir told reporters: "It's not for me to decide who should be fined, but it is for me to say that everybody should follow the rules."
It is not known if either Mr Johnson or Mr Corbyn have received fines.