At its next council meeting in September, members will ease the rules so that more than the 65 per cent of the total funding can be awarded to applicants who cannot afford to raise the other 35 per cent with partnership or sponsorship money.
These rules have made it hard for schools in deprived areas to benefit from the lottery, especially those in cash-strapped local education authorities such as Sheffield.
Wisewood school has already found this out. Maureen Laycock, the acting head of this comprehensive school in a disadvantaged area of Sheffield, was incensed to receive a "bland rejection" for a lottery bid in the same week as John Major announced his sports plans.
The school sought just over Pounds 1 million towards a new sports centre for the school and the community. As there were no firm offers to make up the rest of the cost, the application was turned down. But Ms Laycock had been advised to try to get outline support from the lottery which would then make the bid more credible to sponsors: the proverbial "Catch-22".
She pointed out that Sheffield's potential for education sponsorship through businessindustry links had diminished because of the recession and increasing unemployment. "At Wisewood, we are excellent at innovation and good practice. We have to be, as our dilapidated gymnasium is a mile from the school site, the playing field a five-minute walk away, and facilities include a shared footballnetball yard, a Horsa-hut changing room complete with asbestos, one assembly hall to be shared by PE, drama, examinations and assemblies," she says.
In contrast, Hallamshire Tennis Club, the city's richest, has just received Pounds 550,000 from the National Lottery.
Chris Searle, head of Earl Marshall school in another deprived area with a high Asian-origin population, is struggling to keep afloat the Devon Malcolm Cricket Centre, which he set up five years ago with the help of the Derbyshire and England fast bowler.
"This is one of the few urban centres for the game - and it's the strongest school in South Yorkshire for cricket," he said. Yet at the end of last term the school was reduced to staging a "straight bowling" competition to raise the Pounds 600 needed to rent the ground from the local Caribbean cricket club.
After the second tranche of lottery money was distributed in May, senior council members and some of the 12-strong panel responsible for allocating the funds said they were worried about the lack of applications from poorer areas. Chairman Rodney Walker said members would be looking for ways of helping them within the Government guidelines.
Since then, the Prime Minister's sports initiative, launched last month, has encouraged schools to use lottery money.
But the rules of the sports lottery board militate against this by demanding 35 per cent from outside sources, compared to the arts board which requires 10 per cent. And grants are available only for capital projects for dual use with the community, but not for contingent revenue costs. So the Sports Council would still want reassurance that poorer applicants could afford to run a new sports centre or maintain a new pitch.