Two women who were fined £200 after travelling to a reservoir for a walk around five miles from their homes have had the penalties cancelled.
Jessica Allen and Eliza Moore had said they "thought someone had been murdered" following officers' "heavy-handed" response to a trip to Foremark Reservoir that they believed was legal under COVID-19 rules.
And Derbyshire Police's chief constable, Rachel Swann, said the force had apologised to the women and rescinded their fixed penalty notices following a review.
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"I support the fact that the officers were trying to encourage people to stay local to prevent the spread of the virus," she said.
"This is a responsibility for all of us. We have been working hard to understand the ever-changing guidance and legislation and to communicate this to our officers in a way that makes it clear what is the right course of action to take.
"At present there is no clear limit as to how far people can travel to exercise, but government guidance strongly requests people do not leave their local area.
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"It is important to note that the force has received complaints from residents living in some scenic parts of Derbyshire asking that we carry out activity to stop others travelling to the area because it becomes more crowded for local people."
Ms Allen said at the time that one officer told her a coffee she had brought with her was also against the guidelines - because it counted as a picnic.
But she said in a statement responding to the force's decision that she and her friend were now happy to "draw a line under this event".
"After reviewing our case, our fines have been rescinded and we have received an apology on behalf of the constabulary for the treatment we received," she said.
"We welcomed this apology and we are pleased to draw a line under this event."
It comes as Health Secretary Matt Hancock urged the public not to "flex" the lockdown rules during Monday's Downing Street news conference, saying: "Don't say you're exercising when you're actually socialising."
Derbyshire Police and Crime Commissioner Hardyal Dhindsa welcomed the decision to cancel the fines and called for "clearer direction" for officers on how to apply regulations.
He said: "While the police are doing their absolute best to protect public safety during what is a critical time of the pandemic, the public should rightly expect a proportionate and balanced approach, taking full consideration of individual circumstances.
"We recognise that errors will occur in the face of complex guidance and legislation and it is important such situations are resolved quickly and fairly, as has been the case here.
"There is certainly a need for clearer direction on how the new regulations should be applied in the real world."
Conservative MP for North West Leicestershire Andrew Bridgen said the law must not be "overstepped".
"My two constituents who were fined by Derbyshire police on Thursday for attempting to walk around Foremark Reservoir have had there [sic] fines removed," he said in a tweet.
"The laws must be enforced but not overstepped."
Peter McCall, Police and Crime Commissioner for Cumbria, told Sky News he could not comment on the Derbyshire incident, but conceded "there will be times when it doesn't work well".
"We are dealing with human beings," he said.
He added that a lack of clarity in some of the rules caused problems for police, but said officers had discretion when enforcing restrictions.
"They generally apply that incredibly well," he said.
"Of course there'll be cases where somebody may go over the top or whatever, but that is the position we're in."
