Comic Relief has said it will fund organisations with annual incomes of more than £10m only in "exceptional circumstances".
The new policy, which applies to all of the charity’s open funding opportunities, came into force during a funding call that opened in August, the grant-making charity said.
In a statement, Comic Relief told Third Sector it hoped the move would ensure that its funding made a meaningful difference to the organisations that received it.
Application guidance on the Comic Relief website says: "Unless otherwise stipulated in the funding call, applications made must be by organisations with an income level of between £250,000 and £10m in their last set of accounts submitted to the relevant authority."
But it said the rule did not apply to intermediary organisations that would pass the funding on to smaller bodies.
When an applicant says their annual income is greater than £10m as they fill in the online application form, they are told that Comic Relief funds only those "organisations of your size in exceptional circumstances".
A spokeswoman for Comic Relief said the organisation did not have a "tight definition" of what counted as "exceptional circumstances".
She said. "It will apply on a case-by-case basis and it’s important that we retain the discretion to be flexible about this.
"Open calls are only one of the ways that we make grants – when we are pursuing a more focused goal we may proactively reach out to the best-placed organisations to achieve that end."
Under the new rules, the spokeswoman said, open funding opportunities would "prioritise medium-sized organisations, and we are open to funding direct delivery projects and core costs for these applicants".
She said: "By definition, larger organisations have access to other sources of income, whereas medium-sized organisations often struggle to access the flexible funding they need to become more resilient and grow.
"We are committed to ensuring that our funding makes a meaningful difference to those organisations that receive it. In this way we seek to invest in our partners such that they are left stronger at the end of our funding than at the beginning.
"We also want to fund those organisations that are closest to the context in which they work, informed and led by people affected by issues, and best placed to deliver lasting solutions."
She said there were still some organisations with annual incomes of more than £10m that the charity did fund through other programmes and that Comic Relief would "continue to hold valued relationships with these partners" in the future.
She said Comic Relief had "had many private conversation with some larger organisations affected by these changes and have had a positive response", and the grant-maker had not received any complaints about the issue.