The number of cases rose to 6,200 in the last decade, up from 4,400 in 2001. Two-thirds of the cases are in men.
The condition is often linked to smoking and excessive drinking.
But experts have said the dramatic increase is down to a virus called HPV (human papillomavirus) which can be spread during sex.
Richard Shaw, a Cancer Research UK expert in head and neck tumours, said patients with HPV-related oral cancers tend to be younger and less likely to smoke.