The poll found that breast cancer came out top, with 35 per cent of respondents saying this was a cause they were most likely to support or make a donation to support.
This was followed by lung cancer at 17 per cent and cervical cancer at 9 per cent.
However, other cancers failed to gather much support, with only 2 per cent saying they would support testicular or prostate cancer, 4 per cent backing bowel and brain cancer and no-one at all getting behind mouth or liver cancer.
The British Dental Health Foundation commissioned the research involving more than 800 people across the UK as part of Mouth Cancer Action Month.
The charity said that raising awareness of the risk factors and symptoms of mouth cancer was vital to improving survival rates for the disease, which can fall to just 50 per cent without early detection.
Chief executive Dr Nigel Carter said: “Fundraising is challenging for most charities in the current economic climate and this latest research also indicates there is a clear divide between which cancer causes are most likely to be supported by the public.
“Unfortunately, mouth cancer is one of the least supported causes, despite the number of cases nearly doubling in the past ten years.
“It is important that the public supports campaigns like ours as we strive to save thousands of lives each year.”
Previous figures also show that some types of cancer attract more money than others, though charities funding research say they are trying to address the balance.
Figures from the National Cancer Research Institute (NCRI) show that breast cancer attracted just under 20 per cent of research funding in the UK last year, compared to around 8 per cent for prostate cancer.
But the body said that more than half of all UK cancer research was potentially relevant to all cancers and all cancer patients.
Sarah Cant, from the Prostate Cancer Charity, said: “It is very disappointing that prostate cancer does not rank more highly in terms of cancer causes people would donate to. Unfortunately, despite being the most common cancer in men in Scotland, the disease has traditionally faced a general lack of awareness, as well as a legacy of neglect when it comes to research investment.”