As The TES reported earlier this month, the approach has been piloted in the South West by 24 primary language trainees from the University of the West of England.
The TDA is now to fund more local "learning networks", which will each be composed of a university or other teacher training institution, and representatives from local authorities, primary and secondary schools.
It has picked eight networks already and given each pound;10,000 to explore how subjects such as science and history can be taught in French, German or Spanish. It is inviting applications for further networks.
Advantages of bilingual teaching include the benefit children derive from learning a language in context and the time it creates for it in a crowded curriculum. But it does require teachers to be competent in the language.
The networks will devise a series of lessons to span Years 6 and 7, so secondaries can acknowledge pupils' learning in primaries.
Alex Wilkinson, headteacher of Christ Church Junior in Bristol, which is piloting the method, said: "The level of French those children are using and being exposed to is a lot higher, because it has a real context. But it does need a lot of preparation."
For details, www.tda.gov.ukpartners.