The union welcomes the plan for a co-ordinated London admissions system, with a common application form and timetable, from 2005. But it also argues for a common admissions criteria across the capital without any form of pupil selection, so that schools can achieve a more socially-balanced intake.
Professor Brighouse said such "systemic" changes were not part of the brief he had been given by the Government but that the NUT was right to campaign on the issue.
"I do think a common admissions system will make it far better," he said.
"Until somebody tackles admissions criteria it will remain the case that schools choose children rather than children choose schools."
The NUT's manifesto says many of the Government's London Challenge proposals are deeply flawed, and that the growth of academies and involvement of the private sector is creating problems, not solutions.
Steve Sinnott, NUT general secretary, said: "Educational needs are best met by publicly-provided services which are high quality, free and comprehensive."
His union wants to see a democratically-accountable London education forum.
It would advice on areas where there are gaps in provision such as special educational needs, specialist language provision and teacher professional development.
It also wants more money for London education authorities, teachers to be paid an extra pound;6,000 a year for working in the capital, cheaper housing, a network of training centres and a research centre to support teachers.
Liz Allen, head of Newstead Wood, a girls' grammar in Bromley, south London, took issue with Professor Brighouse.
She said: "London schools already share the Government's new common admissions arrangements aimed at improving secondary transfer. Parents in London value diversity offered by its secondary schools. Oversubscribed schools in London's leafy suburbs already 'select by postcode', which is far less fair.
"Our nine-mile catchment brings a rich and balanced social and ethnic diversity to the school."
Each year more than 700 girls take an entrance exam for one of its 130 places. Last year it came 16th in the London league tables.