Opposition Labour leader Jeremy Corbyn said it was the "responsibility" of governments to minimise the risk of terror by giving police the funding they need after cuts made while Conservative Prime Minister Theresa May served as interior minister.
May and Corbyn had suspended campaigning for a snap June 8 election after the suicide bombing at a Manchester pop concert, which killed 22 people, including children and teenagers, and wounded dozens more.
The issue of security, which was not widely discussed in the general election campaign before the attack, is now expected to feature highly.
However, the poll also suggested that 41 per cent of respondents believe the Conservatives would handle defence and security best, compared to 18 per cent who said the same of Labour.
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YouGov polled 2,052 people on Wednesday and Thursday.
At the launch of the UK Independence Party's manifesto on Thursday, deputy leader Suzanne Evans said May "must bear some responsibility" for the terror attack in Manchester this week due to policing budget cuts.
The Conservatives have been in power since 2010, but Home Secretary Amber Rudd on Thursday said cuts could not be blamed for Monday's attack.
"I have asked the head of counter-terrorism whether this is about resources. It is not," she said.
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