Public Health England (PHE) said people who travelled recently, or plan to travel to Romania, Italy and Germany, and have not had two doses of the MMR vaccine, are particularly at risk.
It said anyone planning to travel to Europe over the Christmas period should check travel health advice.
The comments come after the health body recorded outbreaks in three areas of England - this includes 16 confirmed cases in Leeds, 11 confirmed cases in Liverpool and nine confirmed cases in Birmingham.
Officials said all cases are among children and adults who have not received two doses of the MMR vaccine.
The MMR vaccine is a combined inoculation which protects against measles, mumps and rubella - the full course of MMR vaccination requires two doses.
Measles is highly infectious and can lead to serious complications.
Dr Mary Ramsay, head of immunisation at PHE, said: " The measles outbreaks we are currently seeing in England are linked to ongoing large outbreaks in Europe.
"People who have recently travelled, or are planning to travel to Romania, Italy and Germany and have not had two doses of the MMR vaccine are particularly at risk.
"This serves as an important reminder for parents to take up the offer of MMR vaccination for their children at one year of age and as a pre-school booster at three years and four months of age.
"Children and young adults who missed out on their MMR vaccine in the past or are unsure if they had two doses should contact their GP practice to catch up.
"We'd also encourage people to ensure they are up to date with their MMR vaccine before travelling to countries with ongoing measles outbreaks."
The UK recently achieved World Health Organisation " measles elimination status".
But because of ongoing outbreaks in Europe, the UK will continue to see cases in people who have not been vaccinated and limited onward spread can occur in communities with low MMR coverage and in age groups with very close mixing, PHE said.