People have returned to beauty spots in a "manageable" way on the first weekend after lockdown rules in England eased.
The public was urged to "think twice" before heading to beaches and country parks as councils feared a surge in visitors could result in a rise in coronavirus infections.
Peak District bosses said one area was "extremely busy" but the National Trust said people were being "sensible".
In London, hundreds of people gathered to protest against the lockdown.
This is the first weekend since the lockdown rules were relaxed in England, allowing people to spend as much time outdoors as they want "for leisure purposes", including sunbathing.
There is no longer a limit on how far people can travel and people are also allowed to meet one person outside their household outdoors.
But people in England should not travel to Wales, Scotland or Northern Ireland, where the public is still being told to avoid any travel which is not essential.
Park bosses in the Peak District tweeted that social distancing was "difficult" in the Langsett area at the north-eastern edge of the park, where car parks were full.
"Please don't travel to the area or park outside of designated bays," they added.
The National Trust said that people seemed to be "taking a pragmatic and sensible approach".
"Our car parks which are open are busy, but it's been manageable," a spokeswoman said.
The Lake District National Park Authority's chief executive Richard Leafe thanked the public for "not rushing back" to the Lake District.
He said: "It's early days but at the moment it's quiet and we hope to see this throughout the weekend."
He had previously asked people not to travel "because of the impact you will have on the local communities".
In central London, about 300 people gathered in Hyde Park to protest against the regulations introduced to control coronavirus.
The protesters said they objected to their rights of free speech and movement being curtailed, with some holding several placards and banners including slogans like "freedom over fear".
Police made 19 arrests after trying to get the protesters to move on, including Piers Corbyn - the brother of former Labour leader Jeremy Corbyn.
Ten people were also issued with fixed penalty notices.
Deputy Assistant Commissioner Laurence Taylor said in general people in parks have largely been complying with the restrictions.
He said: "It was disappointing that a relatively small group in Hyde Park came together to protest the regulations in clear breach of the guidance putting themselves and others at risk of infection."
It comes after the Metropolitan Police warned people against taking part in "spontaneous or planned mass gatherings".
It said that "games of football... outdoor concerts or parties, protest, marches or assemblies are still not permitted".
Police have been stopping cars on the A23 between the capital and Brighton, where the local council is asking people to "stay away" from its seafront.
In Glasgow a man has been charged with breach of the peace after a small protest against lockdown measures.
Police Scotland said three warnings had been issued at the city's Queens Park, while there had also been gatherings at Glasgow Green and Holyrood Park in Edinburgh.
An estimated 15 million leisure trips will be made by car in the UK this weekend, an RAC survey suggests.
However, almost half of the journeys will be no more than 10 miles long, according to the motoring organisation's poll of 1,317 drivers.
With sunny weather forecast in parts of the country, the County Councils Network has urged people to stay local.
The network, which represents 36 county authorities, warned that "day-trippers" who travel from towns and cities to exercise were likely to face long queues of traffic and difficulties parking.
And it cautioned that country parks that reopened after lockdown rules were eased on Wednesday may be forced to close again if social distancing becomes impossible.
Julian German, the network's rural spokesman and leader of Cornwall Council, said England's coastal and rural areas "will be there when this is over".
"We are asking households to bear with us and please do their bit over the coming weeks by exercising locally," he said.
"While councils will be allowing cars access to country parks, it does not change the unique situation of the need to maintain social distancing."
He added that the councils wanted to prevent a repeat of the "unprecedented numbers of visitors" to parks and coastal areas over the weekend before lockdown was introduced in March.
The majority of beaches will not have lifeguards after the RNLI suspended lifeguard provision during lockdown - it usually patrol 240 beaches.
Peter Williamson, chairman of Norfolk and Suffolk Tourist Attractions Association, also urged people to stay away, stressing that attractions, car parks and other facilities would be closed.
"What we're trying to say to people is we're not open, please don't come because there is nothing for you here at this moment in time," he told BBC Radio 5 Live.
The Chief Constable of North Wales Police, Carl Foulkes, stressed the rules were different in Wales - where people should only be exercising from their home address - to those in England.
He told BBC Breakfast that officers would be carrying out high visibility controls in key hotspots such as national parks and beaches, as well as road checks to ensure people were complying with the regulations.
Mr Foulkes said vehicles breaking the rules would be told to turn around, with officers using enforcement if necessary.
The warnings come as government scientific advisers say the infection rate in the UK has gone up - and is close to the point where the virus starts spreading rapidly.
The R-number - which represents the average number of people each infected person passes the virus on to - had been sitting between 0.5 and 0.9, but is now between 0.7 and 1.0.
It needs to be kept below one in order to stay in control.
Meanwhile, modelling published by the University of Cambridge and backed by Public Health England, suggests that while London has made the most progress with suppressing the virus, it is proving more stubborn in other parts of England.
The figures do not perfectly match those from the Sage group of government scientific advisers because it assesses multiple models to reach its conclusions.