Patient with “underlying health conditions” dies in Scotland.
The comments prompted confusion over whether the government was saying people who were pregnant should stay at home.
In total there were an estimated 55,000 new cases of H1N1 in Britain last week, although in the vast majority of cases the symptoms were mild.
Speaking to parliament about the national pandemic flu service, Burnham said: “Technology to launch the service has been available for some time.
“But with these latest figures and drawing on advice from the field we have now reached a point where this service is required.
“To act any sooner would have been a distraction to health staff dealing with it.”
Britain has the highest number of confirmed case in Europe and the fifth highest in the world.
Earlier on Monday, Burnham said Britain had “the best preparations in place” to handle the pandemic and was “dealing with it fantastically well”.
Twenty-nine Britons have died from the H1N1 flu virus and officials have acknowledged that they are making plans to cater for up to a third of the population falling ill.