I think its a Lambeth-wide problem rather than just Brixton - I read somewhere that less than 50% of school age pupils who live in Lambeth actually go to school in the borough.
This is due to historic reasons and some selling off of schools for conversion to flats etc - like many problems that have developed over the last 20 or so years the blame can be laid at the Thatcher government's door.
Until its abolition the Greater London Council was reponsible for schools in inner London through an organisation called the Inner London Education Authority - as a result children could go to a variety of schools in the 12 borough inner London area and also ILEA developed many innovative services for inclusive schooling and dealing with the particular educational needs of inner city children which are now mainstream (see for example
http://www.guardian.co.uk/education/2008/jun/03/schools.uk1 for a description of its activities).
When ILEA was abolished the boroughs had to establish education departments which then had to administer the schools in their area and in Lambeth they started off with not enough schools for all the pupils (and a very poor area with a good many pupils with special needs) and the situation has got worse as a result of population growth, financial problems at the councils which has meant they have had to sell of land etc etc etc. And today the only way of getting funding to establish a new schools seems to be through the academies programme.
Interestingly Professor Tim Brighouse last year called for a return of ILEA -
http://www.thisislondon.co.uk/stand.../Academics+call+for+return+of+ILEA/article.do