Fear of a vaccine's side effects is the top reason for people refusing them, a report from the Royal Society for Public Health (RSPH) suggests.
Among parents, this was fuelled by social media, with up to half exposed to negative messages about vaccines.
The Society's report, sponsored by US pharmaceutical company Merck, called for social media platforms and the media to do more to combat "fake news".
Vaccines have saved millions of lives, and side effects are rare, it said.
"The spread of misinformation - if it impacts uptake of vaccines - could severely damage the public's health," said Shirley Cramer, chief executive of the RSPH.
England's chief medical officer Prof Dame Sally Davies recently said parents should ignore myths spread by anti-vaccine campaigners and get their children vaccinated.
What's in the report?
It contains the findings of surveys of nearly 5,000 people across the UK on their awareness and attitudes towards vaccines, such as MMR, the flu jab and HPV.
They include 2,600 parents, 2,000 other adults and more than 200 healthcare professionals, such as nurses, pharmacists and GPs.
What do parents say?
On the whole, the report found parents' attitudes to vaccines were largely positive, with 90% getting their children vaccinated routinely.
In the UK this amounts to 10 or 11 different vaccinations, some with a number of doses.
But roughly one in 10 parents surveyed said they had chosen not to give their child the MMR jab, which protects against measles, mumps and rubella.
The main reasons given were concerns over side effects, followed by doubts over whether the vaccine worked.
For the flu jab, one in five parents chose not to give it to their child while one in 14 refused an HPV jab for their teenage daughter.
Again, those parents expressed worries over unwanted side effects.
Have they got a point?
All vaccines have potential side effects, but they are usually mild such as a headache or tiredness, and affect a tiny number of people.
More serious side effects are extremely rare, equivalent to fewer than one in a million cases, according to the report.
Vaccines have dramatically reduced the number of people suffering with infectious diseases around the world.
They are important right throughout life - from childhood into adulthood and beyond.
What part does social media play?
It can spread misinformation or "fake news" about vaccine safety, despite very good evidence to the contrary, the report says.
People in all age groups said they were more likely to see negative messages about vaccines on social media than positive ones.
Parents can also be heavily influenced by negative headlines in newspapers and online, and it can take a long time to change people's perceptions.
Even 20 years after Andrew Wakefield published his now discredited paper on an alleged link between the MMR vaccine and autism, "Europe is still living with the consequences", the report said.
Anti-vaccine campaigners do not help either. Their messages can lead to misleading discussions around possible side effects and undermine the public's confidence, according to the report.
What does the RSPH recommend?
It wants more education in schools around the value and importance of vaccination, to help bust the myths surrounding vaccines.
It also wants to see vaccinations being offered in different locations, such as high-street pop-ups, gyms and community centres, to encourage uptake.
And it wants the press and social media platforms to clamp down on "fake news".