He told the BBC: "It's quite possible that this will just slowly disappear and that will be the end of it. However, it is possible that this virus could adapt and change more rapidly."
Symptoms of swine flu in humans appear to be similar to those produced by standard, seasonal flu.
The HPA said all those in the UK who have contracted the disease appear to be suffering mild symptoms.
In cases outside Mexico - where officials have revised the number of suspected deaths from 176 to 101 - the effects do not appear to be severe, although the death of a Mexican child has been confirmed in the US.
The World Health Organization, meanwhile, has set its pandemic alert level at five and says it has no immediate plans to move to the highest level of six.
'Wait and see'
A UK schoolgirl, who is among the 15 people to have contracted the virus, is believed to have been on the same plane as the first two Britons to be diagnosed with the disease.
The girl's school - Downend, which is also in South Gloucestershire - will be closed until 11 May and parents have been told to contact their family doctor if any child shows symptoms.
Officials said the two South Gloucestershire cases were not connected.
Another school in Paignton, Devon, also closed its doors this week after it was confirmed a 12-year-old girl had contracted swine flu.
Dr Gabriel Scally, regional director of public health for south-west England, said the decision to close the schools was a necessary precaution.
CONFIRMED & SUSPECTED CASES
Mexico: 101 suspected deaths, 16 confirmed
US: one death, at least 141 confirmed cases
New Zealand: 4 confirmed, 12 probable cases
Canada: 35 confirmed cases
Spain: 15 confirmed cases
UK: 15 confirmed cases
Germany: 4 confirmed cases
France, Israel, Costa Rica: 2 confirmed cases each
The Netherlands, Switzerland, Austria, Denmark, Hong Kong, South Korea, Italy, Irish Republic: 1 confirmed case each
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