The UK is one of the best prepared countries to deal with swine flu and "all action necessary" will be taken to stop its spread, Gordon Brown has said.
He joined a meeting of the emergency committee Cobra by phone from Poland.
Dozens of people across the UK have been tested. It has emerged two people with the virus were back in the UK for five days before entering hospital.
Every UK household is to be leafleted about the virus thought to have killed more than 150 people in Mexico.
The first UK cases are Iain and Dawn Askham, of Polmont, near Falkirk, who had been on honeymoon in Cancun, Mexico.
The Foreign Office is advising against all but essential travel to Mexico, also urging travellers to "consult a doctor immediately if they show signs of flu-like symptoms".
The prime minister said: "I understand the very real concern that people have in Britain and across the world.
"As you know there have been two confirmed cases and I believe that both patients are in better health.
"Let me reassure you that we have been preparing for this kind of scenario for many years."
Iain and Dawn Askham had been on honeymoon in Mexico
Health Secretary Alan Johnson said: "There are no more confirmed cases at this stage, although undoubtedly there will be.
"But all the cases, anywhere other than Mexico, have been very mild symptoms, from which people have recovered."
Justin McCracken, of the Health Protection Agency, said his organisation was ensuring that each suspected case in the UK would receive "very careful treatment and screening".
This is so that "we can do everything possible to increase our understanding of the virus as quickly as possible, and of course to minimise its spread", he added.
The World Health Organization (WHO) 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."
The department has suspended routine consular and visa services at the Mexico City embassy.
CONFIRMED & SUSPECTED CASES
Mexico: 152 suspected deaths - 20 confirmed cases
US: 64 confirmed cases
Canada: 13 confirmed cases
New Zealand: 3 confirmed cases
UK, Spain, Israel: 2 confirmed cases each
Countries with suspected cases: Brazil, Guatemala, Peru, Australia, and South Korea, and seven EU states
The statement said: "British nationals should continue to follow local advice on precautions to take to avoid exposure to the influenza."
Holiday firms Thomson and First Choice cancelled flights to the Mexican resort of Cancun on Tuesday morning - one from Manchester and the other from Gatwick.
A spokesman said: "While we do appreciate that this news may be a great disappointment to customers, we hope they will also understand that their health and safety is of paramount importance to Thomson and First Choice."
The companies said all outbound flights to Cancun and Cozumel would be cancelled, up to and including 8 May. It said it would start repatriation flights for British holidaymakers already in Mexico.
Thomas Cook said all Thomas Cook and Airtours holidays to Cancun have been cancelled for the next seven days.
British Airways, which has four flights a week to Mexico City, said it would not be cancelling any flights.
The health secretary said UK preparations had been going on for the last five years to cope with a flu pandemic.
Passengers flying back into the UK from Mexico saw airport staff wearing masks
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.
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."
But the Conservatives have criticised the government for falling behind with plans to set up a national flu helpline.
The telephone service was supposed to be ready in early 2009 but is not expected to be operational until the autumn.
Shadow health minister Stephen O'Brien has called on the government to "take action quickly".
"The national flu line will be crucial if a pandemic were to happen in Britain, by allowing people to get the information and the anti-virals they will need to fight the flu without having to go to GP surgeries or hospitals," he said.
NHS Direct has stopped call centre staff from booking any new periods of time off until further notice in response to the high expected demand for the service.
There were 57% more visits to the NHS Direct website on Monday afternoon and Tuesday morning compared with the same period last week.
Mr and Mrs Askham are continuing to improve at Monklands Hospital in Airdrie, Lanarkshire, where they are being treated following their return from honeymoon.
Scottish Health Secretary Nicola Sturgeon said the couple were "doing well" but no decision had been taken on when they would be discharged.
Swine flu is a respiratory disease thought to spread through coughing and sneezing
Symptoms mimic those of normal flu. In Mexico more than 150 people are thought to have died from the virus
Good hygiene like using a tissue and washing hands thoroughly can help reduce transmission
She said 23 other people were displaying symptoms across Scotland, but swine flu had not been confirmed.
Nine of those people had been in contact with the Askhams. The other 14 had "travel connections" to Mexico, she said.
It has emerged that the Askhams were mixing with people at home and at work for five days after their return before feeling ill and being admitted to hospital.
The chief medical officer for Wales, Tony Jewell, said there were eight suspected cases under investigation in the nation. All were linked to travel in Mexico, he added.
The Health Protection Agency said it was not releasing details about any suspected cases in England until swine flu was confirmed.
Wiltshire Primary Care Trust has said that seven people are being tested while two cases are under investigation in Derbyshire.
Tests carried out on a female patient at West Middlesex hospital in west London have proved negative.
In Northern Ireland the chief medical officer, Dr Liz Mitchell, said it was likely that there would be cases, although there were none currently under investigation.
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 General Practitioners, 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.
Sir Liam Donaldson's advice on concerns over swine flu
Official 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.
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