The Peak District National Park said the Langsett area at the north-eastern edge of the park was "extremely busy" on Saturday morning, making social distancing difficult.
Visitors seemingly flocked to the area despite people being asked to "think carefully" before visiting national parks and beaches.
On Twitter, park bosses in the Peak District said: "This area [Langsett] is reported to be extremely busy with car parks currently full and social distancing difficult.
"Please don't travel to the area or park outside of designated bays."
With the Met Office forecasting sunny conditions, members of the public are being urged to continue observing social distancing rules and avoid potentially contributing to crowded public spaces.
Since Wednesday, a slight relaxation of restrictions in England means people are no longer limited to one opportunity to exercise outdoors each day.
They can also drive to beaches and countryside beauty spots in England, alone or with members of the same household, and can picnic, sunbathe and relax in public spaces.
But despite the new freedoms, police forces, tourist boards and park authorities across the country urge caution.
On Thursday, Cleveland Police and North Yorkshire Police issued statements alongside the North York Moors National Park Authority asking the public to avoid large gatherings and use open spaces near their homes.
The park authority is carrying out a phased reopening of some car parks and public toilets, but warned most facilities will be closed.
Drivers are asked to "go elsewhere" if they arrive to find a lot of parked cars and people at a particular location.
Assistant Chief Constable Mike Walker, of Cleveland Police, said: "As we move into a new phase of eased restrictions and many of us are now able to spend more time outdoors, personal responsibility is now key.
"Please think carefully about where you are going and how you will be able to keep your distance from others."
Meanwhile, the South Downs National Park has asked people to help keep the local air cleaner by staying home as much as possible and keeping visits to the park car-free.
On a similar note, the Peak District National Park said that despite national guidance changing, people could help give the area "crucial breathing space to recover by staying local".
It also warned that facilities such as toilets, visitor and information centres, cycle hire and hospitality businesses remain closed.
In a statement issued earlier this week, Richard Leafe, the Lake District National Park Authority's chief executive, urge visitors "not to rush back" to the region to avoid putting pressure on the community and mountain rescue teams.
The teams are anticipating an increase in call outs as lockdown regulations are eased and there is a potential surge in visitors to national parks.
Earlier this week, Mike France, senior executive officer of Mountain Rescue England and Wales, said: "Just because the Government says you can go out, it doesn't mean you should."
He encouraged people to make a gradual return to hiking, saying: "No matter how much exercise people have been taking at home, in their gardens or local to home during lockdown, most of them may not be as hill fit as they were three months ago."
With high temperatures of 20C expected in some parts of the country, many people might also be tempted to flock to the coast this weekend.
But the Maritime and Coastguard Agency (MCA) has urged people to stay safe as the majority of beaches will not have lifeguards.
The RNLI suspended lifeguard provision during lockdown and there are currently no lifeguards on the 240 beaches that it normally patrols.
Coastal areas are also deterring visitors from making non-local trips to the seaside.
Malcolm Bell, chief executive of tourism body Visit Cornwall, previously encouraged people not to travel more than an hour from their local area to enjoy the outdoors, and to avoid tourist "hotspots".
Meanwhile, Visit Weston-super-Mare, which has changed its promotional slogan to "don't visit Weston-super-Mare" on social media, is still asking people not to visit the seaside town in Somerset.
In a video posted to Twitter on Wednesday it told people: "Just because you can, doesn't mean you should."
In Brighton the local council is asking people to "stay away" from its sea-front.
Carmen Appich, chairwoman of Brighton and Hove City Council's Tourism, Equalities, Communities & Culture Committee, said: "If thousands of people travel to our city on a sunny day and don't or are unable to maintain safe physical distancing because of overcrowding, this increases the risk of a Covid outbreak and puts everyone at risk."
Meanwhile, authorities in Wales have been reminding the public that lockdown measures are different there and people should avoid all non-essential travel.
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