There were 231 confirmed measles cases in the first quarter of the year, Public Health England (PHE) said.
While this is a drop from 265 in the same quarter last year it was double the 95 confirmed between October and December 2018.
There were also worrying signs of infections in the wider population who may have missed out the measles, mumps and rubella (MMR) vaccine when they were younger.
This would particularly apply to the group of British teenagers and twenty-somethings born in the late 1990s when the now-debunked claim that the MMR jab caused autism was made by disgraced former physician Andrew Wakefield.
Infections have typically occurred in groups which are historically unvaccinated, including religious groups or migrant populations with links to countries with an ongoing outbreak, like the one in eastern and central Europe.
Mumps cases nearly tripled to 795 compared to the 275 during the same period last year, with no new cases of rubella reported.
PHE has urged parents to make sure their children receive the MMR vaccine when offered it or to take it up now if they missed it.
Measles is highly infectious and causes cold-like symptoms and a distinctive blotchy rash a few days later, and while usually mild in children it can cause life-threatening pneumonia or brain damage.
The condition can be more severe for adults, PHE added.
Its head of immunisation Dr Mary Ramsay warned that with measles outbreaks across parts of Europe, families should make sure they are vaccinated before they travel.
She added: “Measles can kill and it is incredibly easy to catch, especially if you are not vaccinated.
“Even one child missing their vaccine is one too many – if you are in any doubt about your child’s vaccination status, ask your GP as it’s never too late to get protected.
“There are measles outbreaks happening across Europe so if you are planning to travel, make sure you check with your GP and catch up if needed.”
There have been 3,789 cases of measles across the Continent during the first three months of this year, according to the European Centre for Disease Prevention and Control. The highest numbers have been in Romania, France, Poland and Lithuania, its latest data from 10 May revealed.
The public health agency said that 94.9 per cent of eligible children aged five received their first dose of MMR in the final quarter of 2018, with coverage of the second doses at 87.4 per cent for children aged five.
To achieve herd immunity for measles at least 90 to 95 per cent of the population needs to be fully protected.
The vaccine is also available to all adults and children who are not up to date with their two doses.