ACT leader John Banks would have trouble retaining Epsom even with endorsement from National, a new poll shows.

A Herald on Sunday-Key Research survey released on Sunday says Banks would be supported by 10 per cent of voters if an election were held tomorrow in Epsom.

But when asked if an endorsement from Prime Minister John Key would affect their decision to vote for Banks, nearly 75 per cent said it would not, the Herald on Sunday reported.

Banks won Epsom for ACT in 2011 largely following the endorsement he received from Key at the infamous "cup of tea" in Newmarket three weeks before election day. A similar endorsement was crucial for Banks' predecessor Rodney Hide in 2008.

Of the 510 eligible voters surveyed, 46.7 per cent said their opinion of Banks had gone down following the debate about donations he received when running for the Auckland mayoralty in 2010.

Mr Banks is under investigation by the police for declaring $65,000 worth of donations to his failed mayoral campaign as "anonymous", despite allegations he knew $15,000 came from SkyCity and $50,000 was from internet mogul and online piracy accused Kim Dotcom.

The survey has a margin of error of plus or minus 4.34 per cent.

If found to have broken the law, Mr Banks would have to step down from parliament, which would force a by-election in Epsom.