Tony Blair told Newsnight he wanted to end fundraising
The survey, conducted by ICM for Radio 4's Today programme, also found that eight out of ten people think the way political parties currently raise their finances makes people 'suspicious of politicians'.
And it showed that seven out of ten people believe rich individuals and big businesses exert too much influence on party policy.
The results will make difficult reading for Tony Blair, who said earlier this week that he would like to put an end to fundraising, but conceded it was unlikely the public would agree to state funding.
Frustration
Just one in four people surveyed said they supported the idea that taxpayers should cover the cost of having political parties.
And despite the opposition to donor influence six out of ten decided it is a price worth paying and the system should not change.
The findings come after the prime minister spoke on BBC 2's Newsnight programme of his frustration over complaints about the way the Labour Party has raised money from big business and trade unions.
He said: "If I could get shot of ever raising a single penny for the Labour Party ever again, would I not do it? Absolutely, of course I would."
But he said he would not condone the move unless there was a consensus amongst the political parties.
Mr Blair said: "You can't have a situation where we as a Government use our majority to push it through.
"And I'm not sure the public would accept it either."
ICM questioned 1,001 people on May 15 and 16 for the poll.