Britain has the largest number of cases in Europe of the potentially lethal virus, rising to 909 in the latest figures compiled by the Health Protection Agency, which has recorded some 50 to 100 new cases daily in recent days.
"In recent days, there have been significant increases in the daily number of cases in certain parts of the UK, most notably Scotland," Burnham said in a statement to parliament on swine flu.
"These increases come as no surprise and are in line with what we know from similar outbreaks.
"But it remains the case that, at some point, we will need to move our focus away from limiting the spread of a localised virus, towards mitigating the effects of a widespread virus."
And he added: "People who have flu-like symptoms shouldn't panic, but stay at home and check their symptoms using the online symptom checker or the swine flu information line."
The World Health Organisation on Thursday announced it was raising its alert level to level six, meaning the world is facing its first influenza pandemic in 40 years.
WHO chief Margaret Chan said the declaration of a "moderate" pandemic should not spark panic and did not mean the death toll from A(H1N1), which currently stands at around 150, would rise sharply.