More than one in 10 children are now estimated to cross council boundaries daily in the capital to get to school, causing serious planning problems for local education authorities.
But while the Liberal Democrats have pledged to overturn the Greenwich judgment of 1989, which ruled that LEAs could not give priority to their own residents, Labour is reluctant to make this change.
"I don't think you can put the genie back into the bottle on parental choice," Margaret Hodge, a member of its education team, told a conference looking at education in the capital this week.
"If you introduce legislation that is seen to restrain parental choice you will be in difficulties."
The Funding Agency for Schools, which shares or has exclusive responsibility for secondary places in 20 out of the 33 London boroughs, reckons that 62,000 pupils cross boundaries to go to school.
Barnet, Bexley, Bromley, Camden, Enfield, Hammersmith and Fulham, Havering, Hounslow, Kingston, Merton and Sutton were net "importers" of pupils. Brent, Croydon, Ealing, Hillingdon, Kensington and Chelsea, Lambeth, Southwark, Waltham Forest and Wandsworth were net "exporters".
Councils claim that parents become "detached" from the boroughs they live in if their children go to school in another local authority and argue there is a lack of democratic accountability.
And while many would like to see a return to an organisation along the lines of the Inner London Education Authority to govern schools in the capital, again they will get no support from Labour.
"We wouldn't go back to the ILEA," Mrs Hodge told the conference organised by the Association for London Government. "It had some strengths but it also had some weaknesses. It was too far removed from what was happening day to day in schools to intervene early and effectively enough to ensure disasters did not occur."
London has one in four of the country's failing schools and education minister Robin Squire told the conference that governors had to get rid of bad teachers.
"London has the best and worst of schools and the best and worst of local authorities . . . if a teacher is weak and can't be improved then the governing body must bite the bullet and take action."
He said difficulties in schools could not be put down simply to funding problems, arguing that there was no link between expenditure and standards.
"If there were, then the best schools in London would be in Hackney, Tower Hamlets and Newham as they are the highest spenders but we know they are not.
"Yes, funding matters, but if you believe it begins and ends with funding you miss the main picture."
However, Maurice Kogan, director of the centre for the evaluation of public policy and practice at Brunel University, said poverty, which is felt most sharply in cities, lined up with an incapacity to participate in and exploit education. "Educational deficits arise not from the incapacity of education to change people, but when social and family backgrounds pull in the opposite direction," he said.
"The gravitational pulls are environmental and familial - poor diet, poverty and poor housing."
Professor Kogan said pupils from poor homes needed study centres and good libraries and that there should be targeted work by schools on parents, possibly through home visits with social workers.
And he criticised the Office for Standards in Education for its attacks on teachers. "One might ask what inducements, other than the purest altruism, there are for teachers to teach in some inner-city schools. Not only real front-line work in unprepossessing surroundings, but also derogation."