Monday, which started this week with a pledge to give charity partners 30 per cent of the proceeds from ticket sales, has been inundated with calls from charities wanting to join. Seventy charities are on the first-round list.
But organiser Chariot will continue to accept only larger charities it believes have the infrastructure to cope with expected donations and are disadvantaged by the National Lottery's grants system. It also excludes all arts, sport and heritage charities because it feels they are well served by three of the four National Lottery distributors.
"We have concentrated on those names the man in the street feels get a raw deal from existing lotteries," said Kim Darton, deputy director of charity partners at Chariot, a rival to Camelot. "We are looking only for mainstream charities that people think are the most in need."
But Kevin Curley, chief executive of the National Association of Councils for Voluntary Service, said: "We hope the organisers will rethink these criteria, which discriminate against most local charities."
Curley said community foundations could have become partners of monday to distribute funds to smaller groups if Chariot had consulted NACVS and set the £500,000 threshold lower.
Luke FitzHerbert, senior researcher at the Directory of Social Change, predicted dissatisfaction among small and medium-sized organisations.
"If monday does succeed, there will be complaints from charities that feel excluded - not least because of sneers being made in the press about wholly proper grants by the National Lottery," he said.