The vaccine: HPV vaccine - brand name Gardasil®
The claim: "Gardasil protects against the two types of HPV, between them responsible
for more than 70% of cervical cancers in the UK." 
Why is it offered to students?
Gardasil is offered free on the NHS to girls up to the age of 18, because, according to the NHS "the HPV virus is very common and is easily spread by sexual activity. As much as half the population will be infected at some time in their life."  Older females and males may also acquire the injections privately.
Although the HPV virus is indeed very common, in the overwhelming majority of cases, it causes absolutely no problems and is cleared by the body naturally.  Furthermore, new evidence is emerging suggesting the HPV virus may not in fact cause cancer at all. A paper recently published in the journal Molecular Cytogenetics showed that all cervical cancer cells investigated during the course of the study contained "new abnormal karyotypes". The genetic makeup of these new abnormal karyotypes indicates the cervical cancers originated with these karyotypes – NOT from a virus. 
In addition, one of the lead developers for the vaccine, Dr. Diane Harper, has publicly spoken out questioning its efficacy. Dr. Harper says young girls and their parents should receive more complete warnings before receiving the vaccine to prevent cervical cancer. Dr. Harper states data available for Gardasil shows that it lasts five years; there is no data showing that it remains effective beyond five years.  That means that were a 17-year-old student to receive this vaccine, any benefit would have worn off by the time they were 22.
Intravenous drug use (28%);
Heterosexual contact with infected persons or multiple partners (22%);
Homosexual activity (9%). 
Furthermore, hepatitis B is not a killer disease for most. Symptoms of hepatitis B disease include nausea, vomiting, fatigue, low grade fever, pain and swelling in joints, which can last for three to four weeks. According to Harrison's Principles of Internal Medicine (1994), in cases of acute hepatitis B "most patients do not require hospital care" and "95 percent of patients have a favorable course and recover completely" with the case-fatality ratio being "very low (approximately 0.1 percent)." 
Read full article on Hep B vaccine