New research suggests that cervical cancer is not actually caused by HPV at all:
http://sanevax.org/hpv-not-cause-cervical-cancer/
HPV probably became associated with cervical cancer because as much as 80% of the population have carried the virus at some time (usually without symptoms) so the two are likely to be found together, but also because they are likely to both be effects of the same cause, i.e. tampon use.
Man-made carcinogenic chemicals are the primary cause of many cancers and it's likely that cervical cancer is one of them. Tampons, especially the extra-absorbent ones, tend to contain such chemicals:
http://integrativewellnessgroup.blogspot.co.uk/2012/01/are-your-tampons-causing-cervical.html
Tampons are also linked to an increased incidence of HPV. It is thought that they allow oxygen to get to the vagina/cervix which the virus needs to replicate.
Of course, since the HPV vaccine is such a money-spinner for the pharmaceutical industry, the HPV-cancer cause-effect paradigm is not likely to go away any time soon.