They were also more likely to agree cats should be kept indoors, with 12 per cent in agreement compared with 2 per cent of cat owners.
But the survey also found the majority of people supported cat control measures after being informed about their impact on native wildlife.
Respondents were told about an Otago University study which estimated 1.12 million native birds were killed by domestic cats every year.
They were then asked whether they would support some form of controls to reduce the future cat population.
The majority agreed, with 19 per cent strongly supporting and 35 per cent supporting some form of control measures.
Almost a quarter were neutral, while 20 per cent were opposed or strongly opposed.
Dr Morgan said he was pleased with the findings, saying education was one of the key reasons for his campaign.
"That's the whole point for me. The initial reaction was, 'Shock horror, he wants to kill all our cats!' And then you go through and you explain to them it's nothing to do with that, it's about wandering cats and this is the damage that wandering cats do.
"And what you find is that people agree with you - even cat owners agree with you."
Dr Morgan said most people agreed there was a problem with wandering cats, but they did not want any of the measures needed to get that result.
To change that, he said people needed to be asked whether they were happy with cats wandering across their properties.
"Because I'll guarantee even cat owners will say to you, 'Like hell I'm not."'
Dr Morgan said most people who approached him in the street - "and there's a lot of them" - were in support of his campaign.
He had enormous confidence in the public.
"Once they get full information on any topic, they're incredibly rational and this topic is no different."
The UMR Online Omnibus survey was conducted between January 29 and February 11 and has a sample of error of 3.1 per cent at the 95 per cent confidence level.