Dr Margaret Chan, director general of the WHO, said that a vaccine could be available in August but it would then take another two or three months for the clinical trial data to be produced.
But speaking on BBC Radio 4, Sir Liam said that the UK was still on course to get 60 million doses of vaccine by the end of the calendar year and that the first supplies would arrive in the early autumn.
Sir Liam also warned that a third of the population of England could catch swine flu by this winter and that the virus could linger for up to five years.
His comments come as a post-mortem reveals that a GP who contracted swine flu before his death died from natural causes.
It is believed that Dr Michael Day had been suffering from heart disease, high BP and had viral pneumonia.
More news from 16 July
GPs lack child protection training, regulator warns
NHS privatisation worries older more than younger people
Electronic prescribing scheme runs in Scotland
Listening event on nurse and midwife future