The charity Unicef said increasing numbers of youngsters are being left at risk.
It said that vaccination rates are plummeting, with inaccurate and misleading anti-vaccination messages on social media thought to be among the reasons.
Public Health England figures show that between April 2010 and December 2018, 2,684 children had not received their first vaccination against measles, mumps and rubella by the age of five.
Two jabs are required by the age of five to provide full immunity, and a further 3,154 children did not receive the second jab.
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It means that the overall vaccination rate over the period was 89% , significantly below the 95% the World Health Organisation says is needed to prevent the disease spreading in the community, and leaving a total of 5,838 children without full protection against measles.
Unicef’s analysis estimated that 169 million children around the world missed out on the first dose of the measles vaccine between 2010 and 2017 – an average of 21.1 million a year.
More than half a million of them were thought to be in the UK.
The most recent figures, for October to December 2018, show that uptake of both doses of the MMR vaccine in England’s five-year-old children is 87%.
There were 966 measles cases in England in 2018, up from 259 in 2017.
Measles is highly contagious.
The symptoms are unpleasant, including a rash and fever, and there can be serious complications in some cases.
The Health Secretary Matt Hancock recently said he would not rule out banning unvaccinated children from schools.
When asked if he would follow measures attempted in France and the US to tackle measles, he said: “I wouldn’t rule out anything but I don’t think we’re there yet.
In America they tried to do this and the courts stopped them so it can be complicated, but really it’s people’s responsibility as a parent to do the right thing – the right thing for their own children as well as, of course, the right of the community that everybody lives in.”
Mary Ramsay, Public Health England’s head of immunisations, said: “The UK achieved WHO measles elimination status in 2017, so the overall risk of measles to the UK population is low.
“However due to ongoing measles outbreaks in Europe, we will continue to see cases, particularly in unimmunised individuals.
“This could lead to some spread in communities with low MMR coverage and in age groups with very close mixing.
“Measles can be extremely serious, so make sure you and your family are protected.”