Mr Lister believes that once the nursery scheme makes vouchers acceptable, there will be a move to extend it to schools and colleges, writes Frances Rafferty.
He said: "Let's rid ourselves of the obsession with class sizes and school sizes. Let's stop protecting the unpopular school. Let's stop holding back the successful school. And let's get ready to welcome a new wave of self-confident, competitive schools that get their money direct from the customer."
Vouchers, he said, would increase pressure on schools to make themselves attractive to parents.
The major problem he foresees is the extra cost of providing vouchers for parents whose children are educated privately.
The vouchers idea has a long history and has been backed by several right-wing think tanks. Sheila Lawlor, former deputy director of the Centre for Policy Studies, said: "It is an idea that should be attractive to all parties. If the money follows the children, it does not become lost in the fog of local government finance."
The response from the independent sector is mixed. David Smith, chairman of the Independent Schools Joint Committee on Assisted Places, said a preliminary survey showed that only one in three heads in the private sector favours vouchers.
"Many would prefer to be able to explore a dialogue with education authorities and make local arrangements," he said.
Graham Able, head of Hampton School, London, is more enthusiastic. He said: "If a voucher scheme was introduced, we would reduce our fees only slightly and would use the vouchers to fund a bursary scheme to allow children whose parents cannot make up the difference to attend if they reach our academic standard. "
Ian Langtry, education secretary of the Association of County Councils, sees the scheme's future depending on the result of the next general election: if the Conservatives win it will be extended, if Labour is in power it will die.