Cumbria Police said the Lake District was among the places experiencing an "influx" of visitors and that people who do not live in the area should stay away.
"A national emergency shut-down of businesses and schools is not an excuse for a holiday," they added in a statement.
West Wittering Beach in Chichester was closed after the number of visitors on Saturday "far exceeded" expectations.
The estate owners said they had seen "an unacceptable movement of people" into the local community.
The MP for Cornwall, Steve Double, has also urged people not to go on holiday to the region amid the COVID-19 pandemic.
He said while he understands people's reasons for wanting to get out of cities, he said it was better to stay at home.
Mr Double told Sky News: "There are reports that roads into Cornwall are full of people with cars full of suitcases and top boxes. People are clearly coming down here.
"Regrettably and sadly some tourist parks are still taking bookings and still urging people to come here."
He added: "I think most reasonable people would consider a holiday at this time, when our country is facing such a huge challenge, as definitely not essential."
Visit Cornwall tourist board said on Friday that anyone who does not live in the area should postpone their visit.
They added: "We urge anyone considering travelling to Cornwall in the coming days and weeks to think carefully about the implications of being removed from your normal social network during the coronavirus period, the risk of not being able to travel back home as planned, to be aware that supermarkets are experiencing the same pressures here as elsewhere, and consider the added pressure on public services in a rural area which this travel may cause."
The warnings come after Mr Johnson ordered the closure of pubs, restaurants, theatres and other leisure places across the UK.
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