Two mothers have lost their fight to stop their daughters being compulsorily vaccinated with the MMR jab.
The case centres on whether the girls should have the MMR vaccine
The women went to the Court of Appeal after Mr Justice Sumner ruled in June the girls, aged five and 10, should be given the three-in-one vaccine against their wishes.
The case was brought by the girls' fathers who want their children vaccinated against mumps, measles and rubella.
The mothers do not want their children to be given any vaccinations - not just the MMR.
Opponents of MMR said the decision was an example of a "big brother bully state", and said at least one of the mothers would continue to fight against the decision.
Lords Justices Thorpe and Sedley and Sir Anthony Evans heard evidence from both sides last week.
Effect on families
Lord Justice Thorpe said the High Court judge's approach had been "above
He added: "What is plain is that ultimately these applications were decided by applying
the paramount consideration of the welfare of the two children concerned."
Lord Justice Sedley said the evidence presented by the mothers in the earlier hearing that the MMR vaccination was dangerous and untenable was "junk science" and "dangerous and unnecessary".
Earlier Elizabeth-Anne Gumbel, representing the mothers who cannot be named to protect the identities of the children, told the court that the High Court judge, Mr Justice Sumner, had not taken sufficient notice of the mothers' wishes and the effect the ruling would have on the families.
It is understood that in both of these cases the mothers are against their daughters being given the three-in-one vaccine because of concerns over its safety.
Some scientists have suggested the jab may be linked to autism and bowel disease.
However, no research has ever proved a link, and the overwhelming majority of experts believe the vaccine is safe.
Mr Justice Sumner ruled it was in the girls' best interests to be given the three-in-one jab.
He rejected the idea of giving the girls separate vaccinations against mumps, measles or rubella, saying that the gap between jabs could put them at risk of getting these diseases.
Both girls in this case live alone with their mothers. Their parents are either divorced or separated.
None of the people involved in the case can be identified for legal reasons.
The British Medical Association backed the High Court ruling. However, it has been criticised by anti-MMR campaigners, including the pressure group Jabs.
Isabella Thomas, a spokeswoman for Jabs, said on Wednesday: "This is not a nanny state but the big brother bully state.
"This could set a precedence for the future and that is our main worry."
She added: "Vaccinations are not compulsory and should never be, We are not blaming the
judge in any way. He was given one-sided evidence in a way."
She urged the pair to fight their case at the European Court of Human Rights.
Ms Thomas said she had spoken to the mother of the younger child.
She said: "She is in shock at the moment, deep shock. She is very, very scared."
But Ms Thomas said the mother had warned she would not accept the court's decision.
Liberal Democrat health spokesman Dr Evan Harris MP said: "On the rare occasions that there is parental disagreement, it is right that the courts should decide based on the best interests of the children concerned.
"Parents should talk to their family doctor about the large amount of scientific evidence which shows that there is no link between the MMR vaccination and autism."
Stephen Foster, the solicitor for one of the fathers, said: "Our client is relieved that his daughter will now receive the protection these immunisations will give her; his major objective has always been protecting her health from diseases which carry a plausible risk of severe illness and death."