Sir Liam Donaldson, CMO for England, said that young children needed to be protected ahead of the next flu season.
'From now on, most deaths from the pandemic flu virus should be regarded as potentially preventable,' he said.
'GPs have the vaccine and stand ready to offer this vital protection. Parents should contact their GP now to make an appointment.'
He added: 'Young children who have the jab now will be protected should H1N1 (2009) influenza return in the next flu season. Pregnant women and those in all other at-risk groups should continue to have the vaccine as well.'
Sir Liam said that, although he had been pleased with the increased uptake of vaccine among the under-fives, deaths in this age group were 'deeply distressing'.
In England, the rate of GP consultations for influenza-like illness was 12.5 per 100,000 population for the week ending 31 January 2010.
The Health Protection Agency overall estimate of the number of cases in the last week remains below 5,000, where it has been for the last six weeks.
The total number of vaccine doses administered to the priority groups in England to-date is 4.25 million (140,000 pregnant women and 404,000 healthy children aged 6 months to under five years in England).