Mr Pirie's call comes in a book, Blueprint for a Revolution, to be published next month, which will be seen as a Thatcherite manifesto for John Major's term of office.
Mr Pirie, an adviser to the Government on the Citizen's Charter, said the 1988 Education Reform Act that allowed grant maintained schools to opt out of local education authority control made insufficient provision for new schools to be established.
He says: 'If an internal market is to work effectively, there must be a mechanism under which bad and unpopular schools would have to close and be replaced by newly started schools which provided the kind of education and environment which parents preferred.
'Many parents feel frustrated because there is often only one good school in the area. Once that is full, the other parents have no real choice, except between the bad and the incompetent.'
Parents and teachers, with local businessmen, should be able to create new state schools where there was demand, Mr Pirie says. They could start cheaply in rented premises.
He suggests the running costs could be met by the Government until they replaced the bad schools, which would close down.
'In a few short years, the initiative will have transformed British education beyond recognition,' he predicts.