But a spokeswoman for the commission said the regulator had opened a case to examine the relationship between the two organisations.
"Given the nature of the concerns that have been raised, on 22 December the Charity Commission opened a regulatory compliance case into the Politics and Economics Research Trust," she said.
"The scope of the investigation is to address the allegations relating to the charity's relationship with the Taxpayers' Alliance."
Matthew Elliott, chief executive of the Taxpayers' Alliance, said: "I am very happy to work with the commission to go through the points that have been raised.
"The claim that we are a front for the Conservative Party will come as a surprise to any of the Tory-run councils that have come under fire from us, and to Conservative Party leaders themselves."