Matthew Hancock, the Minister for the Cabinet Office, accepted a £4,000 donation from the chair of the Institute of Economic Affairs three months before announcing the anti-lobbying clause.
The Cabinet Office referred to the IEA's research on "sock puppets" in the first line of the statement it made announcing the new policy.
Public records show that on 16 November Hancock accepted £4,000 from Neil Record, who became chair of the charitable think tank last March, and that he has received £22,000 from him since 2010.
Record, who runs a currency management company, has made personal donations of more than £330,000 to the Conservative Party since 2005, according to the Tory donations website SearchtheMoney.com.
The Cabinet Office statement began with the line: "The IEA has undertaken extensive research on so-called 'sock puppets', exposing the practice of taxpayers' money given to pressure groups being diverted to fund lobbying rather than the good causes or public services."
Andrew Purkis, a former board member of the Charity Commission, told Third Sector it was unwise of the IEA's chair to put his charity in the position of being perceived as currying favour from ministers through his donations, and unwise of Hancock to accept a donation from someone who was chair of a charity that lobbied government so frequently.
Asheem Singh, director of public policy at the charity chief executives body Acevo, said there was no suggestion anything was improper about the donations, but they did show the danger of the new clause.
A spokesman for the Cabinet Office said in a statement: "The decision to end the farce of government lobbying government was taken based entirely on the advice of civil service officials."
A spokeswoman for the IEA said Record's support for Hancock pre-dated his appointment as chair of the IEA and Hancock's promotion to government. "He has never had any commercial or any other lobbying-type relationship with Matt in any of his ministerial posts," she said. She added that the donation was a personal one and not related to any IEA work.
She said all lobbying carried out by the think tank was done "without a penny of taxpayers' money".