Charities discovered last week whether their bids had made it to stage two of the application process, five months later than they were originally told they would find out.
The BLF predicted there would be 800 applications but received 1,400.
Bidders twice received letters informing them of delays.
Pauline Buchanan Black, director general of the Tree Council, whose bid was rejected, said the BLF should have been better prepared.
"The BLF woefully under-estimated the number of applications, but it's not surprising - second-tier organisations such as ours that build infrastructure are the most difficult to find funding for," she said. "Historic underfunding means it should have come as no surprise to the BLF that it was overwhelmed."
Supriya Horn, fundraising and training consultant at the Directory of Social Change, said the BLF could have avoided delays by issuing applicants with an outline proposal form to filter unsuitable proposals. "The fact that BLF didn't plan for a large number of applications is ridiculous," she said.
Mark McGann, deputy director of policy at the BLF, said the first delay had occurred because of the high volume of applications, and the second was due to high-quality bids that took longer than anticipated to assess.
"We didn't predict the level of complexity created by a number of organisations bidding more than once for different projects," he said.
The Basis programme, which closed for applications last June, offers grants of up to £500,000 to voluntary sector infrastructure projects.