The MMR vaccine remains controversial
However, the government's deputy chief medical officer says that the issue has already been extensively researched both at home and abroad.
A survey for the BBC Radio 4's Today programme found while three-quarters of parents thought the MMR vaccine was safe, more than six out of 10 said parents should have the option of separate jabs for their children.
MMR is a combined vaccine giving protection against measles, mumps and rubella.
Campaigners say it is wrong that parents in the UK are not given the option of three separate jabs for the different conditions.
In rare cases, measles can kill children or leave them severely disabled.
The Department of Health - which is backed by the overwhelming majority of medical opinion - has stressed the combined vaccine poses no health risk to children.
Studies commissioned by the Department of Health, the World Health Organization and public bodies in America have rejected any link between the MMR and disorders such as autism.
Officials say that children are at increased risk of disease if their parents opt for separate vaccines because of the time lag involved.
They have also warned that if children are not immunised with MMR in sufficient numbers the risk of a measles epidemic is sharply increased.
Repeated assurances
However, despite repeated public assurances about the safety of the combined vaccine, it seems that some parents still continue to harbour doubts.
Gillian Brockley, from Connah's Quay, north Wales, chose to travel 125 miles to Worcester so that her daughter could have separate vaccines.
She said: "It should be the parents' choice. If they want it all in one go then fine, but if they don't feel comfortable with that then they should be able to make the choice.
Dr Audrey Boucher, a GP from Whitchurch, Hampshire, said she could understand why some parents still harboured concerns.
"There's a constant drip feed of stories in the press and radio and television about MMR and after BSE who can blame anybody for not believing the government?
"But I'm quite sure that MMR is in the best interests of their child."
Dr Pat Troop, deputy chief medical officer, said: "Obviously when you hear concerns - which we take very seriously - we have gone back and back and back to the research community and all the expert groups to make sure we are offering something that is safe.
"We have had lots and lots of independent inquiries already where everybody's viewpoint, all the evidence has already been reviewed and I'm not sure by going over it all again we would come up with anything different."
Liberal Democrat Health spokesman Dr Evan Harris said: "Scientific research cannot be a slave to opinion polls. Medical research must proceed on the basis of published, properly scrutinised data.
"All the data so far suggests that the MMR vaccine is the safest option."
Rebellious GP
Next month the General Medical Council will hear the case of former GP Dr Peter Mansfield.
Dr Mansfield, 58, was reported to the GMC after he gave children single immunisation jabs instead of the combined MMR vaccine.
He believes families should have the right to choose single vaccinations instead of the MMR jab even though it is recommended by the Department of Health.
Up to 400 children have received the single immunisations from Dr Mansfield at a clinic he runs in Worcester in the past year.
He has also given single jabs to a further 300 children at his practice in Louth, Lincolnshire.
Dr Mansfield was reported to the GMC by a health authority in Worcester, which accused him of putting children at risk.
The survey, carried out by the polling organisation ICM, was based on telephone interviews with more than 1,000 people.