The UK Foreign Office is advising against all but essential travel to Mexico, where swine flu is believed to have claimed almost 150 lives.
Britons visiting or resident in Mexico are being advised to consider leaving.
A couple confirmed on Monday as the UK's first swine flu cases, after a holiday in Mexico, are recovering in a Lanarkshire hospital.
The World Health Organization has raised its alert level to four - two steps short of declaring a pandemic.
Level four means the virus is showing a sustained ability to pass from human to human, and is able to cause community-level outbreaks.
Following the raising of this alert level, a statement on the Foreign Office website said: "Cases of swine influenza have been reported in Mexico City and a number of other locations across the country.
"Travellers should consult a doctor immediately if they show signs of flu-like symptoms."
I don't think people in this country need to be worried at the moment
Professor Steve Field
Chairman, Royal College of Physicians
The department has suspended routine consular and visa services at the Mexico City embassy.
The statement said: "British Nationals should continue to follow local advice on precautions to take to avoid exposure to the influenza."
Health Secretary Alan Johnson said UK preparations had been going on for the last five years to cope with a flu pandemic.
He said the government proposed to use its stockpile of anti-viral drugs to treat patients showing symptoms of the disease, should the virus start spreading in the UK.
Of 14 possible UK cases currently being investigated, all the people involved were well enough to be managed in the community, he told MPs.
Swine flu is a respiratory disease thought to spread through coughing and sneezing
Symptoms mimic those of normal flu - but in Mexico people are beginning to die
Good hygiene like using a tissue and washing hands thoroughly can help reduce transmission
England's Chief Medical Officer Sir Liam Donaldson said: "If a new pandemic does start as a result of this outbreak in Mexico and the United States, we can't make it go away, but what we can do through our plans, particularly our stockpiles of anti-virals, is mitigate its effect."
The couple receiving treatment in Scotland are described as not being particularly ill.
Scottish Health Secretary Nicola Sturgeon said: "I would reiterate that the threat to the public remains low.
The Department of Health (DoH) said surveillance arrangements were being "stepped up" in the UK, without revealing details. It added the outbreak was "unusual and of concern".
Professor Steve Field, chairman of the Royal College of Physicians, said people in the UK were "perfectly safe at the moment", and did not need to start wearing facemasks or stop eating pork.
"I don't think people in this country need to be worried at the moment, the focus needs to be on people coming in from Mexico and other areas where this infection has taken hold," he said.
The World Health Organization Assistant Director General Dr Keiji Fukuda said the higher alert level signalled a "significant step towards pandemic influenza", but added "we are not there yet".
He said the virus had become too widespread to make containment a feasible option, and said countries must focus on trying to put measures in place to protect the population.
On Monday, Mexican Health Minister Jose Angel Cordova said 149 people had died after contracting suspected swine flu - just 20 cases confirmed in that country.
In almost all swine flu cases outside Mexico, people have been only mildly ill and have made a full recovery.
There are fears that the virus has begun to spread around the world:
- There are 40 laboratory-confirmed cases of swine flu in the US, 20 in Mexico, six in Canada, one in Spain, WHO said on Monday
- Tests are also being carried out on individuals or groups in New Zealand, Australia, Brazil, Israel and South Korea who fell ill following travel to Mexico
- A number of countries in Asia, Latin America and Europe have begun screening airport passengers for symptoms, while Germany's biggest tour operator has suspended trips to Mexico
- Several countries have banned imports of raw pork and pork products from Mexico and parts of the US, although experts say there is no evidence to link exposure to pork with infection
UK guidance is that anyone with flu-like symptoms who might have been in contact with the virus - such as those living or travelling in the affected areas of Mexico - should seek medical advice.
But patients are being asked not to go into GP surgeries in order to minimise the risk of spreading the disease to others. Instead, they should stay at home and call their healthcare provider for advice.
Swine flu is usually found in pigs and contracted only by people in contact with the animals.
Mexico: 149 dead - 20 confirmed cases
United States: 40 confirmed cases of swine flu
Canada: 6 confirmed cases
UK: 2 confirmed cases
Spain: 1 confirmed case
UK, Spain, Israel, Brazil, South Korea, Australia and New Zealand: suspected cases being tested