The expansion, which exceeds Government targets, will cost taxpayers pound;113 million in start-up costs in each of the next three years and take the annual cost of the flagship programme to pound;373m.
The Specialist Schools Trust predicts 500 successful applications each year to 2006 after receiving a record 781 bids this year.
It expects there will be 2,963 specialist schools - 93 per cent of 3,200 eligible secondaries - by September 2006, beating the Government target by almost 1,000.
The prediction comes as the Prime Minister and Charles Clarke, the Education Secretary, set out radical measures to raise education standards in London.
The plans include building at least 20 new specialist schools, 30 academies and up to 20 sixth forms or sixth-form centres. Many will replace existing schools. At least 10 - seven of which will be academies - will serve the five most deprived boroughs in the capital: Hackney, Haringey, Lambeth, Islington and Southwark.
Last year ministers set up a pound;3m annual hardship fund to make it easier for schools to find sponsors to bid for specialist status and lifted a pound;150m cap on its own funding. Each specialist school must raise pound;50,000 in sponsorship but will receive a one-off pound;100,000 capital grant together with an annual top-up grant of pound;126 per pupil.
Sir Cyril Taylor, trust chairman, said the increase in specialist schools would lead to a substantial rise in educational standards.
"The record of specialist schools in raising standards makes us optimistic that when most, if not all, schools are specialist then the same success will be achieved across the sector," he said.
Research by David Jesson of York university, based on prior pupil attainment levels, found that specialists have higher than expected percentages of pupils gaining five A* to C GCSEs.
But MPs on the House of Commons education select committee have criticised the specialist schools programme for offering poor value for money. Barry Sheerman, the committee chairman, said he wanted to see careful evaluation to ensure that specialists' success was not just a blip but that they offered consistent improvements.
Sir Cyril revealed that the rules were likely to be changed to make it easier for more schools to take up dual specialisms from one of the present 10. "In 10 years' time the vision is of an entirely specialist system of schools with comprehensive intakes working together in partnership so that pupils could stay in an area and pick the specialism of their choice," he said.
This week Brent Davies, director of Hull university's international leadership centre, warned the Girls' Schools Association's conference that specialist schools represented the greatest threat to the independent sector. "Specialist schools will become selective and therefore change the nature of the school system. They will make it less equitable," he said.
There are currently 1,463 specialist schools covering around 46 per cent of secondaries. They can select 10 per cent of their pupils, according to aptitude, but Sir Cyril said only 6 per cent did.
He expects the majority of the 7 per cent who are not specialist by 2006 to be in special measures or have serious weaknesses or be generally under-performing.
Matt Buck, 31