A child under 16 can consent if they have sufficient understanding and intelligence to fully understand what is involved in a proposed treatment, including its purpose, nature, likely effects and risks, chances of success and the availability of other options.
If a child passes the Gillick test, he or she is considered ‘Gillick competent’ to consent to that medical treatment or intervention. However, as with adults, this consent is only valid if given voluntarily and not under undue influence or pressure by anyone else. Additionally, a child may have the capacity to consent to some treatments but not others. The understanding required for different interventions will vary, and capacity can also fluctuate such as in certain mental health conditions.
I would say most teenagers are Gillick competent to consent, or otherwise, to testing on their own behalf as the possible side effwcts/implications are not complicated or serious. Probably fewer teenagers, but still a good many, and certainly the older teenagers, could be considered Gillick competent for the vaccine also.