Cancer Research UK has attributed the increase to rising rates of the human papilloma virus (HPV) infection, especially through high-risk strains of the sexually transmitted virus.
Two thirds of the 6,200 cases diagnosed in the UK in 2011 were men.
Experts say men are more likely to smoke and drink heavily, both significant risk factors in oral cancer.
But the increase may also be due to rising rates of the HPV infection.
Up to eight in 10 Britons will contract HPV at some point in their lives, but the virus is usually harmless.
Just a few strains cause problems, but one in particular, HPV-16, is known to cause cell changes which could develop into cancer.
There were particularly sharp rises in rates of cancers at the base of the tongue (an almost 90 per cent increase) and the tonsils (around a 70 per cent increase) – two areas of the mouth where cancers are more commonly HPV-related.
Richard Shaw, a Cancer Research UK expert in head and neck cancers based at the Liverpool Cancer Research UK Centre, said: ‘We have seen a rapid increase in the number of HPV16-positive cases of oral cancer.
‘We have also noticed that patients with HPV-related oral cancers tend to be younger, are less likely to be smokers and have better outcomes from treatment than those whose tumours show no evidence of HPV.
‘This raises questions as to exactly how these cancers develop and why they only affect a small proportion of people who are exposed.’
Sara Hiom, director of information at Cancer Research UK, said: ‘It’s worrying to see such a big rise in oral cancer rates.
‘But like many other cancers, if oral cancer is caught early, there is a better chance of successful treatment.
‘So it’s really important for people to know the signs and symptoms of oral cancer – mainly mouth ulcers that just won’t heal, any lumps or thickening in the mouth, lips or throat, or red or white patches in the mouth that won’t go away.
‘It’s not just doctors who have a vital role to play. If you’re worried about any of these symptoms you can see your dentist as well.
‘Dentists have an important role to play in spotting oral cancer early and encouraging their patients to take care of their mouths. So make sure you attend regular dental check-ups.’
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