Almost one in five said they simply did not believe the results of the test.
Most respondents said they felt supported by their family and friends and considered that the future was far better today for those with Down's syndrome.
They pointed to integrated education in particular and a greater acceptance of what it means to be different.
One respondent said: "I don't subscribe to the notion of the 'perfect human being' and found the idea of selecting one child in preference to another abhorrent."
Another said: "I already felt a strong sense of responsibility for my unborn child and knew that I would love it and want it regardless of any additional needs it might have. I knew I could count on friends and family for support."
The survey was compiled to coincide with the BBC Radio 4 documentary Born With Down's.
Carol Boys, chief executive of the Down's Syndrome Association, said the survey showed how much changes in society were influencing people.
She said: "When I and others had our babies it was a very different world - those with Down's syndrome were treated very differently.
"Now there is much greater inclusion and acceptance, with mainstream education having a huge role.
"We think this plays a part in the decisions parents make - there's even been a baby with Down's syndrome on EastEnders."
At the back of our minds we did keep alive the possibility that she might not have Down's syndrome but we knew that we would be able to cope if she did
Following the widespread introduction of pre-natal testing for the syndrome, the number of babies born with Down's fell from 717 in 1989 to 594 at the start of this decade, figures from the National Down's Syndrome Cytogenetic Register show.
But during the current decade the birth rate has increased, reaching 749 births of children with Downs Syndrome in 2006, the latest year for which figures are available.
Down's births have risen by approximately 15% as a proportion of all live births since 2000.
However, Professor Joan Morris, director of the register, cautioned against assuming that many more people were opting to continue with a Down's pregnancy.
She said the rise in the number of babies being born with Down's syndrome was likely to be related to an increase in the number of older women - who are more likely to have a Down's pregnancy - becoming pregnant.
Figures showed that the proportion of women deciding to terminate after finding out their child was likely to have Down's had remained constantly high, at 92%, since testing was introduced.
Quality of life
Frances Dine was 12 weeks pregnant when a scan revealed the condition but she and her husband, Paul, gave little thought to termination.
She said: "Things have moved on and babies with Down's syndrome can have a great quality of life.
"At the back of our minds we did keep alive the possibility that she might not have Down's syndrome but we knew that we would be able to cope if she did - there's so much out there for her.
"Schools are integrated and there are even actors with Down's syndrome.
"There's a worker at our local supermarket who has Down's syndrome and we think that it doesn't need to hold you back."
Born with Down's will be transmitted on Radio 4 at 2000 GMT on Monday 24 November.
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