The Government has rejected calls for the meningitis B vaccine to be given to all children, saying it would be a waste of money.
More than 816,000 people have now signed a petition calling for the jab Bexsero to be given to all children, or at least those up to age 11.
The petition, which is the most signed online petition in parliamentary history, gathered momentum following the death of two-year-old Faye Burdett.
The toddler, from Maidstone, died on Valentine's Day after fighting the infection for 11 days.
Her mother Jenny shared pictures of her daughter just before her death on social media and said the family had endured "a pain you cannot describe".
The plight of meningitis sufferers was also raised by ex-England rugby captain Matt Dawson, who told how his two-year-old son Sam battled - and survived - meningitis C.
The Bexsero vaccine is available on the NHS for babies aged two months, followed by a second dose at four months and a booster at 12 months.
Parents who wish to have older children vaccinated must pay privately, although a worldwide shortage of Bexsero means private stocks are currently low.
In its response to the petition, the Department of Health said its priority was to vaccinate those children considered most at risk from meningitis B.
It said 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: "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."
The Department said the UK was proud to be the only country in the world to introduce a national, publicly-funded meningitis B immunisation programme for babies using Bexsero.
It said the JCVI considered vaccinations for children aged one to four "but did not advise a catch-up programme in view of the marginal cost-effectiveness of even the infant programme".
It added: "There are many bacterial, viral and other causes of meningitis (inflammation of the lining of the brain and surrounding tissues) and septicaemia (blood poisoning).
"Successful vaccination programmes have already reduced the risk of these serious diseases. Current rates of group B meningococcal disease are low. In the early 2000s there were more than 1,600 cases in England, compared to around 400 cases in 2014."
Studies have shown that Bexsero still offers good protection to children who are older when they are vaccinated.
A spokesman for the charity Meningitis Now said it understood the need for further data to be gathered on the duration of protection offered by Bexsero and whether vaccinating teenagers would lead to herd immunity.
But he added: "We are now two years on since the JCVI recommended this study and, whilst we are pleased to read in the Government statement that there is preparatory research that has been commissioned and is under way, we still have no indication of when the full study will commence or be completed by.
"We therefore continue to call for the under-fives to be protected while we wait for the data to be gathered and because of the length of time it is taking to progress the study.
"We keenly await information about the process of MPs speaking to families and health experts prior to a debate in Parliament. We will ensure that we continue to be the voice for people affected by this devastating disease."
On Twitter, GP Neil Bhatia said the vaccine should be given to all under-fives.
But TV doctor Christian Jessen said: "Calls for meningitis B jab 4 all kids rejected as 'not cost effective' I think this is right. Most at risk group IS routinely vaccinated."