Coronavirus: 'Don't rush to beauty spots' plea after PM speech
People have been told to stay away from beauty spots and beaches amid fears relaxed rules allowing longer car journeys would leave areas "inundated with visitors".
Boris Johnson said people could travel by car for "unlimited outdoor exercise" from Wednesday and sit in parks.
Cumbria Police urged people not "to rush to the Lake District" and Visit Cornwall said messages were confusing.
A 50-page supporting document has been published by the government.
Earlier, Foreign Secretary Dominic Raab said people were free to move around within England.
He said: "You can drive as far as you want to, for example, to go and walk in a particular area that you are fond of, as long as you maintain the social distancing."
Some rural areas, including Cumbria and the Lake District, have had relatively high rates of infection and tourism bosses in those areas urged people not to visit.
Cumbria Tourism said it was "shocked by the timing and short notice" of the prime minister's announcement and stressed tourism businesses in the area remained closed.
South Lakes Police said people should "take a long, hard look at your own conscience" if planning to visit the area.
In areas like the South West where infection rates have been lower, there were concerns infrastructure could become overwhelmed if visitors caused the spread to increase.
Mr Johnson announced police would be able to hand out bigger fines to those flouting the rules.
Andy Slattery, Cumbria's Assistant Chief Constable, said he was surprised at the announcement saying it was a "very significant change" for the county and urged people to "still don't rush to the Lake District".
Brian Booth, chairman of the West Yorkshire Police Federation, called the guidance "woolly" and said the announcement had made policing the restrictions "impossible".
The Welsh Government has urged people not to drive across the border into Wales and the UK Government has told people in England not to travel to Scotland.
Visit Cornwall officials said they had been contacted by people asking if they could travel to the county since the speech.
Chief executive Malcolm Bell said it "added more confusion than clarity" and reiterated the message for people to "stay away".
Steve Double, Conservative MP for St Austell and Newquay in Cornwall, said the guidance was "clear" and referred to what was part of people's daily exercise allowance.
"This certainly does not give the green light for people to flock to Cornwall to come and have a holiday or move location to their second home," he said.
In Somerset resort Weston-super-Mare, Tourism Manager Caroline Darlington said it would be "counterproductive to encourage people from further afield to come here when effectively the resort is still closed.
"We are not out of the woods yet and it would be immoral for us to say 'yes, come to Weston, buy your candyfloss'."
Richard Leafe, chief executive of the Lake District National Park, tweeted that the announcement could be "very difficult" for the area and pleaded with people not to "rush to visit us".
In North Yorkshire, Scarborough and Whitby's Conservative MP Robert Goodwill said he had been contacted by concerned constituents, adding "we do not want to be inundated with visitors", according to the Local Democracy Reporting Service.
He added: "I had someone from Castleton worrying that if someone from Middlesbrough decided to go there for a walk, then they pop into the shop and all of a sudden there is a risk of the virus spreading.
"If people can use common sense then the risk is not increased but if it is used by people who do just want to break the rules then it could be dangerous."
The leader of Brighton and Hove City Council Nancy Platts said she was concerned about how residents would be able to maintain physical distancing "if we have an influx of visitors".
While Sarah Butikofer, the leader of North Norfolk District Council - the authority with the oldest demographic in the UK - said any potential influx to the area was "very worrying".
Ray Perry, a director at Rudyard Lake in Staffordshire, said they had been inundated with messages from people wanting to come since Sunday evening.
He said the attraction remained locked down for all activities apart from walking, and they "need clarity" over the guidance.