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Boris Johnson has warned there are signs of a second wave of coronavirus in Europe, as he defended a 14-day quarantine on travellers from Spain.
The PM said the government had to be "swift" - and it would continue to take further action "where it is necessary".
It comes after the Spanish prime minister called the UK's decision to change the rules for Spain "unjust".
Pedro Sánchez said tourists in most regions in Spain would be safer from coronavirus than in the UK.
The UK is advising against all non-essential travel to Spain, including the Balearic and Canary Islands. It also removed Spain and its islands from the list of countries which are exempt from the 14-day quarantine rule.
Meanwhile, Germany has also advised against travel to three areas of Spain.
Speaking during a visit to Nottinghamshire, Mr Johnson said: "What we have to do is take swift and decisive action where we think that the risks are starting to bubble up again.
"Let's be absolutely clear about what's happening in Europe, amongst some of our European friends, I'm afraid you are starting to see in some places the signs of a second wave of the pandemic."
'Stick with guidance'
Asked about reports that the 14-day period could be reduced - as reported by the Daily Telegraph - Mr Johnson said "we are always looking at ways in which we can mitigate the impact of the quarantine".
"At the moment you have got to stick with the guidance that we are giving, we have given the guidance now about Spain and about some other places around the world."
When asked whether the 14-day quarantine period could be cut, transport minister Baroness Vere said the government was "looking at a range of options" including "testing people on certain days" after they arrive.
Ministers are also "certainly looking" at the idea of restrictions on travel to regions rather than whole countries, she said.
Image copyright Getty Images Image caption Spain's rate of infection has jumped in recent daysMr Johnson said if the UK did see signs of a second wave in other countries, it was the government's duty to stop travellers returning and spreading the disease.
"It's vital that when people are coming back from abroad, if they are coming back from a place where I'm afraid there is another outbreak, they must go into quarantine," he said.
"That's why we have taken the action that we have and we will continue, throughout the summer, to take such action where it is necessary."
Scottish First Minister Nicola Sturgeon echoed Mr Johnson's concerns, saying "we are currently seeing a worrying resurgence of Covid" in European countries.
She warned potential travellers not to assume quarantine measures would remain the same at the time of booking a holiday as when they returned, adding: "I wouldn't be booking a foreign holiday right now."
'UK error'
In an interview with the Telecinco TV network, Spain's Mr Sánchez said his government was "talking with British authorities to try to get them to reconsider" the decision.
He said the UK had made an "error" by considering the infection rate for the whole country.
He added that "64.5% of the new cases registered are in two territories" and in most of Spain the prevalence of Covid-19 was "very much inferior to the numbers registered in the United Kingdom".
The rate of infection in Spain is 47.2 cases per 100,000 people, while the UK is at 15, according to the latest figures from the European Centre for Disease Prevention and Control.
While the outbreak remains under control in many parts of Spain, certain areas - in particular Catalonia in the north-east, which includes the city Barcelona, and the neighbouring region of Aragón - have seen a huge spike in infections.
Data up to 19 July suggested there were lower rates of infection in the Balearic and Canary Islands than in mainland Spain.
Speaking to BBC Breakfast, local government minister Simon Clarke said "we've seen a very sharp increase in cases in Spain".
"A 75% increase in cases reported between the middle of last week and the end of last week. That's why we took the action that we have."
On Tuesday, the UK government added Estonia, Latvia, Slovakia, Slovenia and St Vincent and the Grenadines to the list of countries which are exempt from the quarantine rule.
Travellers returning to the UK from anywhere not on the list - including Spain - must now self-isolate for 14 days at a registered address.
People who do not self-isolate can be fined up to £1,000 in England, Wales and Northern Ireland and those returning to Scotland could be fined £480, with fines up to £5,000 for persistent offenders.
Government sources told the BBC that there are no plans to introduce testing at airports, and the priority is to get walk-in centres up and running.
Image copyright Getty Images Image caption In Barcelona, some businesses are quiet as residents are being told to stay at home Image copyright Getty Images Image caption Tourism is important for Spain's economy, with about 18 million trips made by Britons last yearSome travel agents say they are struggling to understand the logic of the UK government's advice.
And MP Chris Bryant, who chairs the all-party parliamentary group for Spain, said: "Why the Canaries - which are further away from Barcelona than Barcelona is to the UK - are on the list as well as mainland Spain, I simply don't understand.
"And there are many, many regions of Spain which have much lower infection rates than many areas in the UK. I think this has been terribly badly handled."
Labour said the government's handling of the restrictions had been "chaotic", and urged it to step in to protect jobs in the travel industry.
"The airline industry and passengers need clarity," said shadow transport secretary Jim McMahon.
Holiday companies Jet2 and Tui were among those to announce sweeping flight cancellations following the UK announcement.
EasyJet, British Airways and Ryanair said they would continue to operate full schedules of flights to Spain, though EasyJet said its holidays would be cancelled for the next few weeks.
Among the thousands affected by the change in travel advice was Tom Clasby, who had checked into an airport hotel near Stansted with his fiancée, their two daughters, and other family members, ahead of a holiday to Majorca.
Mr Clasby, 26, had been due to depart at 06:55 BST on Tuesday.
"We're in a situation where we can't do anything yet and I don't actually know what to do. The poor little girls have been so excited for this holiday - it's the second holiday this year we've had cancelled," he told the BBC.
Image copyright Tom Clasby Image caption "We are just very disappointed, the girls will be so upset," said Tom ClasbyAlso affected was Transport Secretary Grant Shapps, who flew to Spain on Saturday despite knowing a decision on the quarantine policy was due.
Mr Shapps said in a statement he would return to the UK on Wednesday in order to complete his quarantine and would return to work as soon as possible.
It comes as a further seven people with coronavirus were reported to have died across all settings in the UK, according to latest government figures - bringing the UK's total number of deaths to 45,759.
Have your travel plans been affected due to the new government advice? Have you returned to the UK and are facing problems due to quarantine? Are you still stranded in Spain? Share your experiences by emailing haveyoursay@bbc.co.uk.
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