Nearly 70% of voters do not support plans to force internet service providers (ISPs) to disconnect suspected illegal file sharers.
The government has proposed that ISPs be required to cut off users who are suspected of online copyright infringement.
But 68% of respondents to a YouGov poll commissioned by the Open Rights Group said a court should consider the evidence in each case before restrictions are imposed.
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Only 16% of 1,967 adults said they were in favour of automatic internet bans based on accusations.
Jim Killock, executive director of the Open Rights Group, said, "This poll shows people rely on the internet, and an overwhelming majority think that access should only ever be withdrawn as the result of court action. Nearly a third would be much less likely to vote for a party that supports disconnection proposals.
"Only a tiny number - 16% - think the government has got this right.
"Clearly business secretary Lord Mandelson is out of step with public opinion and should think again. MPs should take note, and sign the cross-party Early Day Motion opposing these extreme proposals."
The early day motion was tabled by Tom Watson, the former minister for digital engagement. He is urging the government to rethink the policy. His stance is backed by ISPs, who say the policy would not actually help the problem anyway as illegal file sharers could use someone else's IP address, or encrypt their traffic.