The attempt came when the council, the UK's main refugee charity, was negotiating £9m-worth of grants from the Immigration and Nationality Directorate earlier this year.
The council was asked to agree that if it received the grant, it would allow Home Office officials to approve its press releases and any information it might use for advocacy and campaigning.
"In previous years, they had been more flexible," said Grant Morton, contracts manager for the council. "Negotiations have got a much more rigid structure now.
"They did up the ante this year - that's a good way of putting it. But we were able to invoke the Compact and the response has been quite positive. They didn't seem very aware of it."
The case is being used as an example of the benefits of the Compact, which regulates grants and contracts between government and the voluntary sector. Compact Week, which runs from 1-7 November, is intended to raise its profile.
The grants to the Refugee Council, which gets most of its funding from government, were to provide information and resettlement services for asylum seekers.
A spokesman for the Compact Advocacy Programme said the Refugee Council case was "a textbook example" of a voluntary organisation using the Compact to protect its independence and right to campaign.
A Home Office spokesman said, three days before Third Sector went to press, that he would look into the case, but did not respond in time.