The CRB has begun deregistering charities that are not meeting the minimum annual threshold of 100 applications a year.
Those not registered with the CRB now have to apply through an "umbrella organisation" - larger charities, local councils or private businesses that meet the criteria.
The CRB said charities would be able to find an appropriate umbrella through its online database.
However, one month after the new regulations came into force on 6 April, organisations are struggling to find anyone to do the checks for them.
"Everyone I phoned was either not doing it any more, although they were listed on the website, or they had enough to do with their own applications," said Wendy Fidler, a trustee at the The Dyspraxia Foundation.
When Third Sector made enquiries, a number of entries were found to be incorrect. One example, Welsh Women's Aid, said it had decided against processing applications on behalf of others through fear that it would lead to an "unmanageable workload".
The problems are not restricted to non-registered organisations, however.
One umbrella body, which asked not to be named, said that it was considering revising its decision to process applications on behalf of non-registered voluntary groups because of the volume of requests it has received. "It's been manic," a spokesman said.
The CRB has defended the new system, saying: "A more compact registered body network, working in greater partnership with the CRB and composed of high-volume users, would allow the CRB to focus its resources more effectively."