Other support staff, including teaching assistants and cooks, have been offered 2.475 per cent.
The local government committee of Unison, the biggest union, rejected the joint offer this week. It is set to ballot for strike action starting next month. It says it represents 200,000 of some 500,000 support staff in aintained schools.
Local government employers had originally offered 2 per cent, in line with the Prime Minister's attempt to rein in inflation by clamping down on pay rises.
But they increased the offer as public sector unions threatened co-ordinated strike action that would leave schools without cooks, cleaners and teaching assistants.
There are an estimated 300,000 local government workers at the bottom of the pay scale, whose hourly rate would be increased from pound;5.80 to Pounds 6.00.
The GMB and TGWU unions were still considering the offer yesterday afternoon. Brian Strutton, GMB national secretary, recommended his union drop the threat of industrial action, saying the offer was the best they would get.
The increased pay offer for school support staff gives little immediate hope to teachers. In The TES today, Ed Balls, the Schools Secretary, says pay increases would cause difficulties for the economy.
At the Trades Union Congress national conference next week, the National Union of Teachers will propose a joint campaign of action against the "unfair public sector pay limit".
Ed Balls interview, page 3