A total of 33 per cent of the 1,710 people surveyed said they thought the notes were counterfeit.
Just over three quarters (76 per cent) were unable to identify where the currency was from.
One in six (16 per cent) believed the notes were now out of circulation and around one in 10 (12 per cent) said they were unsure of the exchange rate between Scotland and England.
Nearly a quarter of respondents (23 per cent) would reject the notes.
A total of 17 per cent thought Bank of Scotland notes to be fake, dropping to 16 per cent for the Clydesdale Bank.
Jordan Ferguson from Censuswide said: “We have seen the Scottish currency debate building a lot of momentum across the country, with celebrities and politicians raising questions around the acceptance of Scottish bank notes.
" As a research consultancy, we wanted to find out why there was such an issue with Scottish notes being accepted in England. Our findings show a number of people living in England are unable to tell if Scottish notes are in circulation; with other respondents considering the currency to be fake or out of circulation. These issues may be playing a role in the rejection of bank notes by businesses."
Earlier this month, Liberal Democrat MP Alistair Carmichael lodged a Private Members' Bill in the House of Commons in a bid to make it legally binding for Scottish banknotes to be accepted across the UK.
Scottish banknotes are legal currency in the UK but not legal tender.
No banknotes are classed as legal tender in Scotland and the Royal Mint explains the phrase is a narrow technical term referring to the settlement of debts, and in ordinary transactions both parties can agree to accept "any form of payment".
Mr Carmichael's Legal Tender (Scottish Banknotes) Bill would mean no distinction could be drawn between Scottish banknotes and others in the UK as forms of payment.
An earlier attempt to legislate for Scottish banknotes to be accepted throughout the UK was made by current Scottish Secretary David Mundell.
His Scottish Banknotes (Acceptability in United Kingdom) Bill was put before the UK Parliament in 2009 but was not made law.