More than £18,000 was spent by Bristol City Council researching whether there was a demand for an Islamic school.
The MORI report showed there was strong support among Muslims for such a school and that the council should address the issue, or disappoint parents.
The Bristol Islamic School Trust (BIST) asked the authority for funding for the school, but was refused despite the findings of the 2004 research.
The council said such investment was not possible at the time.
"[We] had already closed seven secondary schools to address the level of surplus places and had already committed around £264m to rebuild the remaining secondary schools and a new secondary school in north Bristol," a spokeswoman added.
The Andalusia Academy in St Pauls celebrated its third annual fund-raising event on Sunday, having been set-up by BIST in 2005.
It receives no money from the council or government and is funded by fees of £2,500 per year for secondary pupils and £1,500 for primary pupils, as well as fund-raising events and donations.
BIST asked for official funding after launching its campaign during the council's recent secondary school review process.
Its own research found there was a significant need for an Islamic school.
The council said it then commissioned the MORI report to "better understand the concerns of those community groups who had asked the council to consider establishing a Muslim faith school".
The number of pupils attending the school has doubled in a year
In conclusion, the MORI report stated: "Support for an Islamic school and awareness of the BIST campaign are at such a level within the Muslim community that the Council cannot afford not to address this issue without significantly disappointing parents."
The survey did not address the feasibility of establishing a new school, a council spokeswoman said.
Dr Ghassan Nounu, chairman of the BIST board, said that the school would like to be state-funded.
"There are state-funded Islamic schools nationally which are open to everyone.
"The focus is not to teach an Islamic education - but on an environment that makes students comfortable and focuses on learning."
He said the school was currently short of £3,000 a month needed to pay back a £500,000 loan, and it needs £300,000 to expand the school, which has a waiting list for its reception class.
It also hopes to find a two to three-acre site on which to build an academy school for pupils who need "more room to work and play", said Dr Nounu.
The council said its policy is to "support and promote diversity in its school provision within the resources available".
But it added that improving existing schools was the "immediate priority" in relation to academies.