UK residents are being advised by the Foreign and Commonwealth Office against all but essential travel to Mexico.
The fresh advice came as the World Health Organisation upgraded its pandemic threat alert over swine flu.
The EU health commissoner previously issued a warning against travel to affected areas.
It came in advance of two British tourists, who were staying in the Mexican resort of Cancun on honeymoon, as being confirmed as having swine flu.
And cruise ships on western Caribbean itineraries are having itineraries switched away from Mexican ports.
The FCO said people travelling to Mexico should consult a doctor immediately if they show signs of flu-like symptoms.
UK travellers should also avoid large crowds, shaking hands, kissing people as a greeting or using the subway while visiting the country, where at least 100 people are thought to have died after contracting the disease.
EU health commissioner Androulla Vassiliou, quoted by the BBC, said: "I’d try to avoid non-essential travel to the areas which are reported to be in the centre of the cluster to minimise the personal risk and to reduce the potential risk to spread the infection to other people."
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by Phil Davies
