Eleven of the 1009 people surveyed thought Buzz Lightyear was the first person on the Moon.
The Toy Story film character was named alongside Louis Armstrong. Eight of those taking part thought the late jazz musician made the first moon walk.
Not quite three quarters correctly answered that Neil Armstrong took the first step onto the Moon.
Eleven per cent of people polled thought the Apollo programme was a recent as the 1980s, with just 68 per cent knowing that the first moon landing took place in 1969.
A total of 44 per cent considered the missions to be a waste of money.
The survey was conducted for E&T magazine, published by the Institution of Engineering and Technology.
Editor in chief Dickon Ross said: "The Apollo moon landing is mankind's most outstanding engineering event so it's deeply worrying that such a large number of people should think the first moon walk never happened and that the public's belief in the legitimacy of science and technology seems to be declining over time."
Conspiracy theorists have pointed to a number of flaws in the pictures and footage from the Apollo missions as proof that the moon landings were staged.
For instance, the US flag planted by Neil Armstrong and Buzz Aldrin was said to be waving in a breeze, which should not have been possible on the airless moon.
Nasa's response was that the flag waved a little when deployed due to residual momentum from contact with the astronauts, not because of windy weather.
Alleged light and shadow anomalies were the result of the highly reflective surface of the Moon and the wide-angle cameras used by the astronauts, said the space agency.
Another question mark over the lack of dust kicked up by the lunar module was explained by the fact that the craft's rocket exhaust fired out sideways rather than straight down.
Leading space scientist Professor John Zarnecki, from the Open University, said: "I think it would have been a far greater achievement to have mocked the whole thing up AND to have kept it quiet for four decades.
"If one in four Britons today don't believe the moon landings ever happened, then I'm afraid that says a lot about one in four Britons. And what it says isn't very complimentary."
He pointed out that moon rocks brought back to Earth by the Apollo astronauts were very similar to those returned by a series of unmanned Soviet probes.
Veteran astronomer Sir Patrick Moore said about those who believe the moon landings were a hoax: "If ignorance is bliss they must be very happy."
and I started with the fake moon rocks. telling eh?
I am good at throwing it too!
the lovely beard