It is a warning that Webster, a virologist known as the "pope of bird flu", has been sounding for more than 50 years, initially to the scepticism of his peers but to growing respect more recently. The virus that keeps Webster awake at night is H5N1.
The bird flu virus first emerged as a public health risk in 1997 when it caused 16 human infections and six fatalities in Hong Kong, prompting Margaret Chan, Hong Kong's then-director of public health and now director-general of the World Health Organisation (WHO), to close the territory's wet markets and initiate a mass poultry cull.
But it was the return of human infections in Thailand and Vietnam in 2003 and outbreaks on chicken farms in Asia, the Middle East and Eastern Europe in 2005 that made H5N1 a household name, while the 2009 H1N1 swine-flu outbreak prompted the WHO to declare a pandemic.
"We were extremely lucky in 2009," Webster says. "Nature didn't put in the killer genes, that's all."
At the same time, he insists, the threat from H5N1 has not gone away.
On the contrary, if the latest scientific data are to be believed, a new "mutant" strain of the virus, codenamed 2.3.2., has already moved from China and Vietnam to central Asia and eastern Europe, spread by migratory waterfowl.
Meanwhile, in H5N1 "hotspots" such as Egypt, where another variant is endemic in the poultry industry, the virus continues to kill people in significant numbers.
As Webster told an international gathering of flu experts at St Hilda's College, Oxford, this month: "It's only a matter of time before it comes to the Americas."
But perhaps Webster's greatest contribution to science lies in his insight that pandemics begin when avian and human flu viruses exchange genes to form a new strain - one that people lack the ability to fight. Webster, a fellow of the Royal Society, calls this process "viral sex".
In the past 100 years, it has happened four times. The first and worst instance was in 1918-19 when an H1N1 virus caused a pandemic that killed an estimated 50 million people. In 1957 and 1968, it happened again, resulting in 1 million to 4 million deaths.
The most recent reassortment event was in 2009, when a virus distantly related to the 1918 pandemic strain caused a worldwide alert.
Despite having invested millions in disease surveillance since the 90s, Webster says the virus caught flu-watchers with their "pants down".
But the broader public remains, for the most part, uninformed.
With around 18,000 deaths from swine flu worldwide to date - about half the number who die from seasonal flu in the US every winter - scepticism over the threat of a flu pandemic is at an all-time high.
"When bird flu gets to the US, however, I predict people will wake up to the need for vaccination pretty quickly," says Webster.
Since 2003, H5N1 has infected 565 people and killed 331, a mortality rate of close to 60 per cent. It has also killed or forced the culling of more than 400 million domestic poultry and cost an estimated US$20 billion ($25 billion). But the UN's Food and Agriculture Organisation said its biggest concern was the appearance of the new 2.3.2. group of viruses in China and Vietnam, and the associated risk that migratory waterfowl could carry the virus further afield.
Webster believes the focus on 2.3.2. is premature. He is more worried about the related 2.2.1 strain endemic in Egypt's poultry industry (with 32 human infections and 12 deaths already this year, the highest of any country in the world).
Webster says we need to know more about wild birds' role in perpetuating viruses in the wild.
But for now, Soderbergh's film may prove the best way of galvanising action. With its lingering shots of viruses attaching to seemingly innocent objects and its apocalyptic scenes of social breakdown, Contagion has been hailed as a "grown-up bio-thriller for modern times".
And Webster acknowledges that "to the extent that it may scare people, it could be useful".
"What people don't appreciate is that H5N1 has already been the cause of a chicken apocalypse. Once it learns to go human to human, there'll be no stopping the damn thing."
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