Downing Street has defended Boris Johnson for riding his bicycle seven miles from home, saying he complied with Covid rules during his trip.
Labour accused the prime minister of having double standards, after it was reported he had been spotted in the saddle at east London's Olympic Park.
Government guidance says daily outdoor exercise is allowed but people should not travel outside their local area.
The PM's spokesman said any suggestion he had broken the rules was "wrong".
But he did not confirm whether Mr Johnson had been driven to the Olympic Park from Downing Street or cycled there.
Metropolitan Police Commissioner Dame Cressida Dick told BBC Radio 4's Today programme the trip had not been "against the law - that's for sure".
People should go for exercise "from your front door and come back to your front door", she said, adding: "That's my view of local."
The prime minister's press secretary said the Commissioner's words were "wise".
"The instruction is to stay local and for her a reasonable interpretation was to exercise from their front door but for some people it's more complicated. Everyone needs to exercise their own judgement", she added.
The Evening Standard reported that the prime minister had been seen in the Olympic Park, with his security detail, on Sunday.
There's nothing in English lockdown law that says Boris Johnson shouldn't have pedalled around London's Olympic park on Sunday, seven miles from Downing Street.
But this comes at a time when the government is desperately pleading with people to take Covid-19 seriously and follow the rules.
In England that means leaving home only for essential work, shopping and exercise. The guidance also says "stay local" without defining how far people can roam.
Travel for exercise is allowed "a short distance within your area" to access an open space.
Number 10 will insist that's precisely what Mr Johnson did.
But his ride highlights the problem everyone faces trying to interpret rules, and relying on people using common sense.
The outing certainly doesn't help ministers straining to tell the public - in clear, consistent, easy-to-understand terms - to stay at home.
Andy Slaughter, Labour MP for Hammersmith, west London, criticised the prime minister for having a "do-as-I-say, not-as-I-do" attitude.
Speaking to Today, Policing Minister Kit Malthouse said: "What we are asking people to do is when they exercise to stay local.
"Now local is, obviously, open to interpretation, but people broadly know what local means.
"If you can get there under your own steam and you are not interacting with somebody... then that seems perfectly reasonable to me."
The PM's official spokesman added: "We have always trusted the public to exercise good judgement. We did throughout the first lockdown and continue to do so."
The issue of travelling for exercise was highlighted at the weekend after police in Derbyshire fined two women £200 after they drove five miles from home to take a walk - a penalty that was later dropped.
Government advice for England says people can leave home to exercise, but adds: "This should be limited to once per day, and you should not travel outside your local area."
The guidance adds: "Stay local means stay in the village, town, or part of the city where you live."
The government also states: "The law is what you must do; the guidance might be a mixture of what you must do and what you should do."
In Scotland, the advice is that exercise can be taken if it "starts and finishes at the same place, which can be up to five miles from the boundary of your local authority area".
In Wales, exercise also has to start from and finish at home. There no limits on distance travelled, although the advice is that "the nearer you stay to your home, the better".
People in Northern Ireland are advised not to go more than 10 miles from home when exercising.