The deadly swine flu virus could infect up to 40% of the UK population in the next six months if the outbreak becomes a pandemic, world health officials said.
Professor Neil Ferguson, a member of the World Health Organisation (WHO) taskforce which decided to raise its alert over the virus to level four, said four in 10 people could be infected if the country is hit by a pandemic.
But Prime Minister Gordon Brown said Britain was "among the best prepared countries in the world" and added that the Government was taking "all the urgent action that is necessary" to help prevent the spread of the virus.
Mr Brown also said he will take part in a meeting of the Government's Cobra emergencies committee.
Earlier, Britons were warned to avoid all but essential travel to Mexico as the WHO said the deadly swine flu virus can no longer be contained and raised its alert to two lower than the maximum of six, signifying a "significant increase in risk of a pandemic".
Prof Ferguson, of Imperial College, London, said cases were likely to die down within a matter of weeks because the UK was moving out of the normal season for flu infection, but may flare up again once the summer was over.
He told the BBC Radio 4 Today programme: "We don't really know what size epidemic we will get over the next couple of months. It is almost certain that, even if it does fade away in the next few weeks - which it might - we will get a seasonal epidemic in the autumn.
"We might expect up to 30%-40% of the population to become ill in the next six months if this truly turns into a pandemic."
The first two British cases were confirmed on Monday and more suspected infections emerged.
The two confirmed patients, Iain and Dawn Askham, of Polmont, near Falkirk, had been on honeymoon in Mexico and were being treated in isolation at Monklands Hospital in Airdrie, Lanarkshire.