"The targeted vaccination group of 12-year-old British schoolgirls are at no risk of contracting cervical cancer. Cervical cancer is an extremely rare disease.... by the time there is any risk for these schoolgirls any effect from the vaccine [if there ever was one] would have worn off".
Getting HPV now is how you contract cervical cancer later. If we can prevent the HPV infection, we can prevent the cancer. And if we can prevent it in enough girls, we can stop the chain of infection, and essentially wipe out HPV among the vaccinated groups.
In fact, countries with high vaccination rates (Denmark and Australia, see http://hpv.kegel.com/warts/#campaign ) are seeing a decrease of 90% in genital warts among girls ages 16 and 17 -- the age groups that were vaccinated when they were 11 or 12.
And Victoria, Australia is seeing a drop of 50% in positive pap smears among girls under 20 since vaccination started. ( See http://www.vccr.org/downloads/VCCR_stat_report_2011_FINAL.pdf ).
Cancer takes longer to develop than genital warts, so it'll be another 5-10 years before we see mortality rates fall, but given the drop in positive pap smears, there is little doubt among the science-based medicine community that that will happen.
So yes, girls are at risk of starting the long path to cervical cancer if we don't immunize, and yes, immunizing now will prevent the risk later.
But there are so many inaccurate statements in the article that it'd be hard to address them all.