The Shaw Trust is threatening to terminate suppliers' contracts if they do not adhere to its equality and diversity policy.
The trust provides employment services to people who find themselves disadvantaged in the labour market because of disability, ill-health or social circumstances.
A spokesman for the trust said: "We feel our suppliers should adhere to the same standards we set ourselves. In many cases they probably already do, but we want to see actual evidence.
"Their policies should cover recruitment, and their buildings should be accessible to people with disabilities.
"We did not set out to wield the cudgel, but if a supplier does not comply, we will seriously have to think about whether we want to continue to have a relationship with them. Equality is our raison d'etre."
The spokesman added that the trust hoped other charities would follow its example.