At present procedures for removing teachers can take up to nine months. Professor Barber said it should take two months, from when a head first tells someone that they are not up to the job.
Successive ministers have said that it should be easier for schools to get rid of bad teachers, and both Tony Blair, the Labour leader, and David Blunkett, the party's education spokesman, have said that governors are taking too long to dismiss bad teachers but have not put a time limit on the process.
Professor Barber, dean of new initiatives at London University's Institute of Education, said: "The procedure for getting rid of bad teachers is too cumbersome and slow. Schools ought to be able to complete it in a couple of months and still allow for all the appropriate appeals and due process."
Speaking at a conference at the institute, he said schools and local authorities were making big strides in school improvement. But removing incompetent teachers was a vital part of rescuing failing schools, and the collection of evidence about poor performance often delayed the operation.
Governors and heads are responsible for taking action against poor teachers so central government's influence is limited. From September school inspectors will report confidentially to heads on the best and worst teachers.
Labour has said that it intends to discuss with local authorities and teacher unions how poor teachers could be dismissed more quickly without jeopardising staff rights. It believes the present process fails to strike the right balance.
Professor Barber said: "Teacher unions would benefit if they were leading the advocacy for streamlining procedures against incompetent teachers. Lots of their members and the public want to see them working towards improving quality."
Nigel de Gruchy, general secretary of the National Association of Schoolmasters/ Union of Women Teachers, said: "Bad teachers can already be sacked within two months. It is only incompetent managers who can't get rid of incompetent teachers."
He said that teachers had to be given between five and 10 days' notice of dismissal. If there was an appeal, that would take another five or ten days.
"For a person who is marginal, it might take several months. For someone who is a disaster, the information should be readily available if heads and governors have been doing their jobs properly." Prevention, he said, was better than cure. Governors should not employ weak teachers in the first place.
Chris Woodhead, the Chief Inspector of Schools, has estimated that there are currently 15,000 incompetent teachers. He believes the present rules which prevent appraisal reports being used as part of disciplinary proceedings should be re-examined.