The number of reported cases dropped slightly during the Christmas week but this was in keeping with dips at the same time in previous seasons, the HPA said.
John Harris, an expert in norovirus from the HPA, said: "As we have seen in previous years there has been a dip in the number of confirmed laboratory reports owing to the Christmas and New Year period. However, in line with other norovirus seasons we will expect to see an increase in the number of laboratory reports in the next few weeks.
"Norovirus is very contagious, and anyone who has had it knows it is very unpleasant. If you think you may have the illness then it is important to maintain good hand hygiene to help prevent it spreading. We also advise that people stay away from hospitals, schools and care homes as these environments are particularly prone to outbreaks."
Cases of norovirus shot up earlier than expected this winter across Europe, but experts have been unable to determine why this is the case or predict whether numbers will continue to rise at the same rate.
Symptoms - which usually last a few days - include sudden vomiting, diarrhoea, or both, a temperature, headache and stomach cramps.