A survey by the HIV charity Terrence Higgins Trust found more than 20% of people aged 18 to 24 mistakenly thought there was a cure for HIV.
Among the same age group almost a quarter believed condoms have holes in them which let HIV through.
And more than one in ten young people thought the virus could be passed through kissing.
This is only a theoretical risk, and possible only if both parties have open sores, cuts or bleeding gums which bleed into each other. There has only been one suspected case of HIV being passed on in this way.
The poll of 1,000 adults was carried out to mark 25 years since the death of Terry Higgins, whose battle with Aids inspired friends and colleagues to set up the charity.
The results showed that ignorance about the virus were not confined to the younger age group.
Across all age groups, 28% of people either thought that condoms had holes in which let HIV through, or said they did not know.
Twelve percent thought that sharing cutlery carried a risk of HIV transmission, and 10% thought you can be infected through sweat.
Only one in three people who were surveyed said they thought they had received good sex education at school.
Much confusion
Nick Partridge, chief executive of Terrence Higgins Trust, said: "It's frightening that 25 years after Terry Higgins' death, this level of confusion exists.
"The lack of good sex education means many young people are leaving school ignorant about HIV and safer sex.
"HIV is now the fastest growing serious health condition in the UK, and there is no cure. It's time to get our facts straight."
Terry Higgins was among the first people to die from an Aids-related illness in the UK.
Since his death in 1982, more than 17,000 others have died from Aids-related diseases and there are now more than 70,000 people living with HIV in the UK.
More people than ever before were newly diagnosed with HIV in 2006.
Groups most at risk of HIV in the UK continue to be gay men and the African community.
Anti-retroviral drugs can keep HIV in check for most people who take them.
But there is growing concern that the drugs will become increasingly ineffective, as HIV - which can change its structure with astonishing speed - evolves ways to combat their action.