Future Systems' proposals for the Geoffrey Chaucer Technology College would see most of the 1958 building - by the architects behind the Barbican - flattened.
The move has won the support of English Heritage because the school is in 'special measures', a situation that is at least partially blamed on its buildings.
The conservation quango is also in support because Future Systems is retaining some of the best elements of the school, including the pentagonal assembly hall, which will be restored as part of the construction work.
This part of the project ( pictured), has an unusual engineering solution that allows for 1,300m 2space, free from central supports, covered by a hyperbolic paraboloid roof made up of five concrete shells.
The demolition job will include the rest of the CPB buildings on the site, that include a four-storey classroom block and another four-storey building of 'practical rooms'.
The move comes as another Chamberlin Powell and Bon building faces the wrecking ball. The City of London is backing plans to demolish Milton Court, an unlisted adjunct to the Barbican estate.