The Government has rejected calls for the meningitis B vaccine to be given to children of all ages, saying it would not be cost effective for the NHS.
More than 815,000 people have now signed a petition calling for the jab Bexsero to be given to all children, not just newborn babies.
But in a response to the petition, the Department of Health said its priority was to vaccinate those children considered most at risk from meningitis B.
It pointed out it was following guidance from the Joint Committee on Vaccination and Immunisation (JCVI), which advises the Government on the cost-effectiveness of vaccinations.
The statement said: "With this programme, our priority is to protect those children most at risk of Men B, in line with JCVI's recommendation.
"The NHS budget is a finite resource. It is therefore essential that JCVI's recommendations are underpinned by evidence of cost-effectiveness.
"Offering the vaccine outside of JCVI's advice would not be cost effective, and would not therefore represent a good use of NHS resources which should be used to benefit the health and care of the most people possible.
"When any new immunisation programme is introduced, there has to be a cut-off date to determine eligibility.
"While this is extremely difficult for parents whose children aren't eligible, there is no other way of establishing new programmes to target those at highest risk without introducing inequalities."