My local health authority made it clear that they were willing to go to the mats with vaccine denialists. The roll out when HPV vaccination started about five years ago (initially Cervirix, more recently Gardasil) was also to Y9 and Y10, and the authority made it perfectly clear that if your parents were shouting about teh vacinez then the authority were willing to give it to you anyway on the basis of Gillick/Axon competence. Indeed, I think they put on the consent letter "if you refuse consent, your daughter can seek the vaccination herself and it would be our general policy to provide it" or words to that effect. Certainly, nurses were saying that.
I know of at least one girl at my children's school who did just that, and I believe/suspect there were others.
That would be harder in the case of a Y8 pupil, I suspect, at least if a doctor didn't want to be on first name terms with their defence union rep. But if a 14 year old rocked up to their GP's surgery and simply said "I want the HPV vaccination, even though my mother Has Views" then the doctor would be on pretty safe ground to take a judgement on her ability to appraise risk and benefit and provide it over her parents' head. And if a doctor were approached over contraceptive advice by a child claiming Gillick/Axon competence, they would arguably be remiss in their duty of care to not also ask about, and offer, HPV vaccination.
After the comprehensive legal beatdown delivered in the wonderfully titled "The Queen On The Application Of Sue Axon v The Secretary Of State For Health (The Family Planning Association: intervening) [2006] EWCA 37 (Admin)" it's unimaginable that a complaint about such a policy by a parent would get anywhere.