The Department of Health (DoH) has said surveillance arrangements are being "stepped up" in the UK.
Among the UK cases was a 62-year-old female Canadian visitor to Sale, Greater Manchester, who was taken to hospital as a precaution after showing flu-like symptoms.
NHS Northwest says the tests on the woman in Manchester have proved negative, and her case has been downgraded to being an unspecified viral infection.
Mr Johnson also 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.
He added: "People will wish to know whether they should wear facemasks.
"Although we are aware that facemasks are being given out to the public in Mexico, the available scientific evidence does not support the general wearing of facemasks by those who are not ill, whilst going about their normal activities."
Alan Johnson: 'The UK has been preparing for a flu pandemic for five years'
And Mr Johnson said preparations had been going on to cope with a flu pandemic for the last five years.
"We have established a stockpile of enough anti-virals to treat more than 33 million people, that is to say half of the UK population," he said.
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, 26 in Mexico, six in Canada and one in Spain, the World Health Organization (WHO) said on Monday
Tests are also being carried out on individuals or groups in New Zealand, Australia, Brazil, Britain and Israel who fell ill following travel to Mexico
The United States and the European Union have urged travellers to Mexico to exercise caution
WHO experts have raised the global pandemic alert level from three to four on a six-point scale
EU Health Commissioner Androulla Vassiliou said: "I'd try to avoid non-essential travel to the areas which are reported to be in the centre of the cluster in order to minimise the personal risk and to reduce the potential risk to spread the infection to other people."
England's Chief Medical Officer Sir Liam Donaldson said a potential pandemic would mean "many many more people becoming ill than occur every winter with the normal seasonal flu".
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
He added: "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."
UK Foreign Secretary David Miliband said it was "right that we put the issue of swine fever on the foreign ministers' agenda" because there needed to be "maximum European co-ordination" on the issue.
The Health Protection Agency (HPA) has a procedure for confirming whether or not a patient has swine flu.
If a patient rings their GP or NHS Direct to report symptoms, they will be told to stay at home, not to visit a surgery or hospital.
The HPA has prepared an "algorithm" - in essence, a flow chart - for suspected cases. On the phone, or possibly even face-to-face depending on the circumstances, the patient's GP or NHS Direct will take the patient through the algorithm.
If the answers to the algorithm lead the questioner to believe the patient may have swine flu, a sample will be taken that will then be sent to one of the HPA's network of regional labs for testing.
If the sample is confirmed as influenza type A, it will then be sent to the HPA's Reference Lab at the Centre for Infections in Colindale, where they will carry out genetic typing on it and establish whether it is a confirmed case of swine flu.
There have also been cases of swine flu reported in Canada and a suspected case in France.
Medical correspondent Fergus Walsh sees what UK scientists are doing about swine flu
However, no-one outside of Mexico has yet died, leading to suggestions that the severity of the cases there may be due to the strain mixing with a second unrelated virus circulating in the community.
UK-based pharmaceutical firm GlaxoSmithKline said it had supplied 100,000 packs of flu drug Relenza and 170,000 additional doses of its seasonal flu vaccine to the Mexican authorities, at their request, since the outbreak began.
Swine flu is usually found in pigs and contracted only by people in contact with the animals.
The DoH said they could not yet give details of what the "stepped up" surveillance arrangements were and that meetings were ongoing, adding that the outbreak was "unusual and of concern".
Professor Steve Field is the chairman of the Royal College of GPs, which heads research into flu in the UK.
He says the coming days will be crucial in assessing the scale of the threat to the UK if people do contract swine flu.
He said: "We'll know a lot more... tomorrow and by the end of the week.
"What we've got to try and do is stop people who've come in from Mexico, places where this is prevalent, going to their GPs and spreading it amongst vulnerable people. That's what's really important this week."
In trading on the London stock market, shares in British Airways were down 7.4% and Thomas Cook fell 4.3% on fears over the economic impact of the swine flu outbreak.
Mexico: 149 dead - 26 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, Australia and New Zealand: suspected cases being tested
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