A Downing Street spokesman would not confirm if Mr Johnson had been driven to the park, but said he had complied with Covid-19 guidelines.
The remarks came after Labour accused the Prime Minister of hypocrisy over the incident on Sunday when Mr Johnson was seen cycling in Olympic Park, seven miles away from his home.
Official regulations brought in by Mr Johnson say that exercise is limited to once a day and you should not leave your local area, in a bid to halt the surge in coronavirus cases.
Asked about Covid restrictions Mr Hancock was pressed on whether people should exercise seven miles from their home - thought to be a reference to the reports concerning Mr Johnson.
"We have always trusted the public to exercise good judgment throughout the pandemic when we have asked them to exercise locally".More news: Did YouTube Bar Trump From Posting New Videos to His Channel?
Government guidance says daily outdoor exercise is allowed but people should not travel outside their local area.
Mr Johnson's press secretary Allegra Stratton, asked if Mr Johnson regretted his bike ride, said: "He will.be doing bike rides again - you all know how much he loves his bike".
However, Dame Cressida did call for for greater clarity on Covid regulations. That's my view of local."But some people will need to get in a vehicle to get over three dual carriageways to get to where they're going to walk the dog".
A source told the Standard that Johnson was out exercising at the time, adding, "But he did note how busy the park was and he commented on it at the meeting last night".
Asked about the PM's bike ride, Ms Dick told BBC Radio 4 that "stay local" is a "relative term" with no exact definition, adding that Mr Johnson's trip was "not against the law".More news: Saved By The Bell Vet Dustin Diamond Has Been Hospitalized
"That's my view of local".
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. It is complicated. I understand that.
"If there are too many people breaking this rule then we are going to have to look at it". It's quite a lot and I think it will encourage more people to recognise we are in a health crisis.
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".More news: US State Department Cancels UN Envoy’s Trip to Taiwan