Reported cases of human papilloma virus (HPV) - thought to cause about 80% of cervical cancers - have fallen sharply since girls were given the vaccine.
But the Joint Committee on Vaccination and Immunisation (JCVI) found little evidence to justify treating boys too.
Critics said vaccinating boys could help reduce the risk still further.
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Across the UK, all girls aged 12-13 are offered HPV vaccination as part of the NHS childhood vaccination programme.
Mary Ramsay, head of immunisation at Public Health England, said: "Evidence from around the world suggests that the risk of HPV infection in males is dramatically reduced by achieving high uptake of the HPV vaccine among girls.
"While there are some additional benefits to vaccinating both males and females, the current models indicate that extending the programme to boys in the UK, where the uptake in adolescent girls is consistently high (over 85%), would not represent a good use of NHS resources."
This initial recommendation by JCVI will now be subject to a public consultation and a final decision will be made in October.
The British Dental Association said it would urge the committee to reconsider the evidence.
The chair of the BDA, Mick Armstrong, said: "HPV has emerged as the leading cause of oropharyngeal cancers, so JCVI's unwillingness to expand the vaccination programme to boys is frankly indefensible."
Shirley Cramer of the Royal Society for Public Health said: "We are deeply disappointed by the JCVI's decision today, which suggests that fundamental priorities are focused more on saving money than on saving lives.
"Such a simple vaccination programme has the potential to make such a big impact on the public's health on a national scale.
"We hope that the government's advisory committee reconsider this decision as soon as possible and put the public's health and wellbeing before cost-saving."
The argument for vaccinating boys HPV
Source: HPV Action
A decision not to vaccinate boys against a cancer-causing sexually transmitted infection has attracted fierce criticism.