Half did not think condoms should be given to under-16s
Most people would like measures to change people's behaviour to cut rates of sexually transmitted infections, a BBC poll suggests.
ICM conducted the nationwide phone poll of 1,010 adults in England, Wales and Scotland between 20 and 22 August.
Most thought the government should intervene to discourage sex among under-16s.
But more than a third thought their sex lives were their own business and would only want information on STIs.
'Target under-aged sex'
The number of people being diagnosed with a sexually transmitted infection is at record levels, official figures show.
The BBC's Healthy Britain poll shows people want action to tackle the problem.
Some 86% agreed the government should impose tougher restrictions on sexual images on children's TV and in magazines aimed at children in order to discourage under-aged sex.
Nine out of 10 people aged 18-24 thought it was right that the government tries to make people change their behaviour on STIs.
But, overall, a third of the adults questioned said they would not want the government to interfere in their own sex lives, apart from to provide information about the risks of casual sex and infections.
Nine out of 10 supported TV campaigns and publicity to promote safer sex and highlight the risks of unprotected sex.
The same proportion supported more information about sex and relationships in school to discourage under-aged sex.
But three out of 10 thought less of this type of information was key to discouraging sex among under-16s.
Eight out of 10 said the government should spend funds on providing free condoms.
But half did not believe these should be provided to people under the age of 16.
Most supported government making it easier for people to get screening and treatment for STIs by providing more money for sexual health screening services.
Just over 70% supported government spending funds on campaigns to discourage people from having casual sex, versus 26% against.
Women are more supportive of campaigns against casual sex ¿ 81% versus 62% of men.
About 64% of 18-24 year olds support campaigns against casual sex, while 79% of 55-64 year olds support campaigns against casual sex.
A spokeswoman from the Department of Health said the government was committed to improving the country's sexual health and tackling the rise of sexually transmitted infections and had already taken great steps to this end.
"Sexual health services suffered from under-investment over many decades. We've already ploughed in millions of pounds to support the sexual health strategy - the first ever such action plan in this country.
"The Government has committed £35m investment since 2002 to help fund modernisation of GUM clinics and reduce waiting times."
But Dr Vivienne Nathanson from the British Medical Association said: "It is clear from the BBC poll that the public wants more government action to promote sexual health and reduce the soaring rates of sexually transmitted infections.
"More resources are needed to ensure that sexual health clinics can meet government targets and see patients within 48 hours.
"It's pathetic that some people are acting responsibly by trying to find out if they have contracted a sexually transmitted infection only to be told that have to wait six weeks for an appointment."
She said national awareness campaigns promoting safer sex were also needed.
"And not only campaigns that last a couple of months but long-term campaigns that will help alter people's behaviour and which understand that it is not only teenagers who are at risk," she said.
Anne Weyman, chief executive of the Family Planning Association, said: "There is enormous support from the public for an effective school-based education programme to prepare young people for their adult lives.
"The government really needs to address the serious issue of access to quality services and importantly, equipping people with the information they need to make responsible choices to protect their sexual health."
ICM conducted a nationwide phone poll of 1,010 adults between 20 and 22 August.