Britain is Europe's worst-hit territory, with estimates of 55,000 new cases last week, and both British Airways and Virgin Atlantic said they have put in place measures to turn back passengers showing symptoms.
"If we have concerns about a customer or the customer is concerned, then we have a 24-hour medical service we can call to give advice to staff," said a British Airways spokeswoman.
"There have been a number of cases where we have advised customers not to fly on the basis of their diagnosis or symptoms of H1N1."
Britain's health authorities are advising people with symptoms to delay journeys if they are feeling unwell.
"If there are signs of something being wrong, be it excessive sneezing or coughing, not looking well, high temperature, then the airport staff can call in a medical team for extra advice," added Virgin Atlantic spokesman Paul Charles.
"If the medical team believe there are reasons not to fly, the passenger will be asked to produce a fit to fly certificate from their doctor or a hospital, and they will be put at our cost on to the next available flight."
The news of more stringent checks came with a group of 52 students and teachers in quarantine after the British Council said four students tested positive for the A(H1N1) virus upon their arrival in Beijing for a study tour.
Later Sunday, the BBC said on its website that another four British school pupils from the same group had been confirmed as having swine flu following tests.
"It was a bit of surprise to be detained at the airport. We have been in a state of shock," Ian Tyrrell, one of the teachers leading the tour, told AFP by telephone from the hotel where the group was quarantined.
Tyrrell said there were some Americans and other nationalities under quarantine at the hotel, some of them students, but he could not provide a specific number.
He added that two of the children who tested positive for swine flu had since rejoined their groups in quarantine, while two others were "doing well" in a Beijing hospital.
China, which has registered around 1,500 positive cases of the virus, has launched aggressive measures to try and detect swine flu, including temperature checks on foreign flights into the country.
While the World Health Organisation has stopped collating figures on infected numbers, European Union Health Commissioner Androulla Vassiliou predicted Saturday that 60 million people across the 27-nation bloc would need priority vaccination.
Northern France, next to the Channel crossings into England, has seen an upsurge in new cases over the past week -- and Italy has warned that the start of the next school year could also be put back.
The spread of swine flu shows no sign of abating, with Egypt reporting its first death linked to the virus on Sunday after a 25-year-old woman returning from Muslim holy places in Saudi Arabia died in hospital.
Egypt's top cleric or mufti, Sheikh Ali Gomaa, said he would not issue a decree barring Egyptians from making the pilgrimage, but health officials said all returning pilgrims would be quarantined.
New cases were also confirmed Sunday by Moroccan health authorities and in Russia, where a sailor back in port became the ninth person infected since the end of May.
In the last table released by the WHO on July 6, the UN agency had recorded 94,512 laboratory-confirmed cases in 136 countries and territories since April, including 429 deaths.