The site for the new secondary school development for young people with learning disabilities is to be located on Hanworth Road, Feltham.
Hounslow Council is now inviting organisations from Multi-Academy Trusts to specialist charitable organisations to place their bids to run it.
All submissions are to be made by November 24.
The chosen site is already owned by EFSA (Education and Skills Funding Agency) and will offer places for children with social, emotional and mental health needs.
Currently, the majority of dedicated SEN places are provided by special schools in the borough.
Applicants for those who are interested in running the school must set out how they will be able to meet the specification for each project.
The requirements for bids have been developed with the Department for Education to meet the needs of the local community and provide SEN places for pupils.
Councillor Tom Bruce, cabinet member for education, children services and youth services at Hounslow Council, said: “Free schools are currently providing good places right across Hounslow.
“Due to the continuing rise in demand, I would urge specialist organisations to apply in order to help us increase our provision and meet the needs of the community."
The specification document and application forms are available to download at Hounslow Free School Competition.
A total of 19 local authorities have invited applications as more than 1,600 new special free schools places will be created across England.
The closing date to submit a bid is 12pm on Friday November 24, 2017.
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