Forecasts of pupil numbers for 20 out of the 33 London boroughs where the FAS shares or has exclusive responsibility for secondary places disclose that they will rise by up to 15 per cent by 2003.
Rates of increase vary greatly between areas with the lowest predicted in Bromley (6.7 per cent) and the highest in Bexley (27.3 per cent).
An FAS report on the supply of secondary places in the capital highlights particular difficulties for outer London boroughs, where a net shortage of places is predicted.
Problems are expected to be most acute in Bexley, Enfield, Sutton and Waltham Forest, where the authorities will be short of between 1,030 and 2,730 basic-need places by 2003.
At best, the report suggests, there will be a deficit of 9,600 places for 11-16 year-olds across the 20 boroughs - at worst it could be 22,500. Most of the extra places are likely to be provided by expanding existing schools and a number of projects to achieve that are already under way.
But the FAS also says new schools could be built in Bromley, Ealing, Enfield, Hillingdon and Sutton.
And it has given its backing to Virgo Fidelis, an independent girls' school in Upper Norwood in Croydon, gaining grant-maintained status. The borough has a slight shortfall in girls' places.
The 9,600 shortfall - which would cost Pounds 62 million to remedy - is based on the Department for Education and Employment's method of calculating basic need (the requirement for additional school places where there is no more capacity).
Using its "more open enrolment" system which provides a measure of the physical capacity of the school, there would be a shortage of 22,500 places.
Forecasts of the rise in the 11-16 population in London from 1996 to 2003 far exceed those for the rest of England.
The London Research Centre anticipates a 10.9 per rise, while the Office for National Statistics puts it higher at 13.1 per cent. Across England as a whole, the ONS predicts an increase of just 8 per cent.
London is a key area for the FAS - one in five of all GM secondary schools are in the capital, while almost a third of its pupils are in opted-out schools. The average for England is 20 per cent.
Its report - the first in a series - has upset the Association of London Authorities which believes a York-based body cannot possibly plan schools which will meet the needs of local communities.
"A strategic authority for London, working with every local authority in the capital, would be ideally placed to identify what London's children need, " said Sheila Knight, ALG education chair.
"The FAS has offered a Polaroid snapshot which is full of holes and already well out of date. This shows that the Government was quite wrong in relying on a quango to attempt a job that was clearly beyond it."
What the report does show is the high level of movement across LEA boundaries - in 1994 a total of 62,000 pupils (16 per cent of the 11-16 resident population in London) lived in one borough but went to school in a different one.
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".
Sir Christopher Benson, chairman of the FAS, said the report confirmed that planning in London needed a wide-angled lens.
"It is not enough to see it through the eyes of individual local education authorities. These additional 10,000 places need to reflect what London parents want, both in type and location."