The research found Sharia finance was shown to be understood widely in this country.
It comes after David Cameron's recent announcement of plans for Britain to become the first Western country to issue a sovereign sukuk, or Islamic bond.
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Some 60% of those surveyed said it was relevant to all faiths and 65% understood the way Islamic banking works is different to the conventional way.
The system involves Islamic banks paying profits rather than interest on savings products, charging rent, not interest, on their home finance products.
Some 57% of those surveyed, which included Muslims and non-Muslims, understood it worked this way.
Sultan Choudhury, managing director of Islamic Bank of Britain, which commissioned the research for its 10th anniversary, said: "The insights come at a time when the UK Islamic finance sector as a whole is set to embark on several important developments.
"This includes the launch of a sovereign sukuk, due later this year."
Some 66% of respondents described Sharia finance as appropriate in a modern western society such as the UK.
However, only 9% of Muslims said they use Sharia compliant finance exclusively.
Some 36% of Muslims use it already and a further 45% said they are very likely to consider doing so in the future.
Mr Choudhury said: "The bank has broken new ground by conducting this research, which will shape how the retail market for Islamic finance evolves."