The Institute of Cancer Research poll of 2,000 people found more than a third do not use sunscreen when sunbathing.
The incidence of melanoma skin cancer will treble in the next 30 years, with climate change likely to exacerbate the problem, they warned.
Experts said people needed to know most cases of skin cancer could be avoided.
The Institute's SAFE campaign found that 60% of those questioned are more worried about skin cancer now than they were 10 years ago.
But despite the widespread concern, 35% of people do not use sunscreen when sunbathing.
One in 10 said more should be done to educate people about the dangers of skin cancer.
And only just over half (52%) could identify the signs and symptoms of the disease.
Climate concern
More than 75,000 new cases of skin cancer are diagnosed in the UK each year, a figure that is rising.
Experts also warn that climate change may cause the number of cases to increase even more dramatically than predicted.
Professor Richard Marais from the Institute of Cancer Research said: "There is growing concern about climate change and its long term effects on the weather.
"If this leads to more sunshine then it is likely that the incidence of skin cancer, which is caused by overexposure to UV light, will rise at an even more alarming rate."
"These results reflect the fact that people are deeply concerned about skin cancer, but that many people still do not know how to look after their skin.
"It is vitally important that everyone is aware of how to protect themselves from the harmful rays of the sun."
He added that most cases of skin cancer could be avoided and treated if caught early enough.
Rebecca Russell, manager of Cancer Research UK's SunSmart campaign said: "Skin cancer is one of the most common cancers in the UK and the number of people diagnosed each year has more than doubled since the early 80s.
"Up to eight in 10 skin cancers could be prevented by being SunSmart, so it's very important to be aware of how to enjoy the sun safely.
"Sunscreens can help to protect against skin cancer, but they're not enough on their own.
"In strong sunlight, our best advice is to use factor 15+ sunscreen, seek shade between 11am and 3pm, cover up and take care not to burn."