Speaking at the 21st anniversary celebrations of the British Screen Advisory Council at London's Mansion House, he said the new organisation would be a "21st-century National Trust for talent in Britain, backing human capital rather than buildings."
NESTA would be launched with National Lottery funds after the millennium and built up with gifts or assignments of copyrights and patent royalties in the same way that the National Trust encouraged endowments of land and property.
In the meantime, Mr Blair said he wanted the Dearing Committee on Higher Education Funding to address the anomaly that discriminated against dance and drama students in the award of maintenance grants.
He reminded his audience, which included Lord Attenborough and Sir David Puttnam, of his passion for education. "A just society and a strong economy depend on the excellence of the education we provide our children. Yet arts and education feed off each other. Schools and colleges are the source of artists and audiences of the future."
The marriage of education and technology had enormous potential, he said. His party already had plans to link every school to the information superhighway, to bring down access charges, and to improve teacher training. Labour's plan to create a National Grid for Learning would bring the treasures of Britain's museums to children all over the country. "Children in Newcastle should be able to tap into the treasure trove of the VA and the National Gallery."
Labour would also bring more artistic expertise into education by encouraging the expansion of theatres' and orchestras' outreach work and bringing in other artists as associate teachers.
He wanted British, not American companies, to teach English "the jewel of the cultural industries", round the world. "We have great broadcasters, we have telecom companies, we have the Open University, we have the British Council - let's see them work together to help the English language reach more people and create new markets for our cultural industries."
Mr Blair made a passing reference to sport "because of its importance to education, television and the work of the Department of National Heritage".
"We deplore the Government's policy of forcing local authorities to sell off school playing fields, thereby denying millions of children the opportunity to develop their sporting potential. This is a policy we are committed to reverse."
He said Labour did not see the DNH as a "tiresome drain. It is a department of jobs and wealth as well as enjoyment."