Chief executive Brian Durrant said that BT had not been able to lay cable fast enough to meet demand from the many schools wanting to join the network, as each one needed new cable laid.
As an interim solution, he said schools are being offered ADSL to provide access to the Grid until they can be connected by fibre.
A decision to use fibre links only was taken last year to ensure the network could cope with schools' future demand for bandwidth.
But despite starting a year later than the other regional grids, Mr Durrant said 20 per cent of London schools had a broadband connection by the end of August and he expected 40 per cent to have one by August this year.
Mr Durrant admitted there had been problems with the Canadian-based Netsweeper filtering system, which used artificial intelligence to assess web pages, but said they had now been resolved.