Doug McAvoy, general secretary of the National Union of Teachers, said he was surprised and dismayed to see that under the education Bill schools which partially select will still be able to do so.
The Government has also been criticised for saying specialist schools will be able to choose up to 10 per cent of their pupils by aptitude, just one year after research by Michael Barber, now head of the Department for Education and Employment's standards unit, showed present tests to be flawed.
David Blunkett, the Education and Employment Secretary, famously told the Labour party conference: "Watch my lips, no selection by exams or interviews under Labour."
The School Standards and Framework Bill says selection will be allowed by grammar schools, those which have partial selection, or those wishing to select by ability for banding.
Margaret Tulloch, executive secretary of the Campaign for State Education,said: "I'm horrified at the amount of potential selection from a Government supposed not to believe in it."
The NUT has welcomed the ability to select by banding, saying it has worked well in a number of local authorities, including the London boroughs of Greenwich and Lewisham.
Schools' admission criteria can be challenged, but Mr McAvoy believes this gives too much power to the adjudicator to pronounce on whether partial selection will end. The other concern is that because grant-maintained schools are disproportio nately partially selective, the resulting foundation schools will be as well.
The Government has championed specialist schools and sees them playing a role in education action zones. But research into the admissions procedures at city technology colleges, published last year by Professor Barber, then dean of new initiatives at London University's Institute of Education, showed the tests were unreliable and more research was needed on ways to measure aptitude for specialist education.
The Local Government Association said it would be looking closely at the Education Secretary's code of practice to ensure it spelt out the role of the adjudicator.
It was also claimed this week that thousands more pupils would be thrown out of school because of Government plans to remove local authority powers to overturn exclusions, writes Dorothy Lepkowska.
Education authorities claim that the Bill removes their rights to block permanent exclusions made by headteachers and governors, which will lead to a sharp rise in the number of children being thrown out. Between 12,500 and 14,000 a year are excluded from schools.
Graham Lane, education chairman of the Local Government Association said the changes would result in "an explosion" of 30,000 youngsters roaming the streets". He said the LGA and the National Children's Bureau were seeking an early meeting with Stephen Byers, the school standards minister,to urge the Government to reconsider.
The clause will bring in line the majority of schools with those in the grant-mainta ined sector which already operate beyond the remit of local authorities.
Under existing legislation schools have to submit proposals to exclude a child to the local authority, which can overturn them.
Parents will retain their right to appeal, but authorities would no longer be able to veto an exclusion before it reached that stage.
Estelle Morris, the education minister, said: "The Government's priority is to avoid exclusions in the first place, therefore our approach is based on early intervention rather than mopping up after exclusions have occurred. Our proposals will mean the local authorities will now have a role to make arrangements for appeals for all schools and be able to express their views at the appeal."