The chief executive of the Charity Commission has written to all 118 charitable think tanks telling them to "retain balance and neutrality in their research work".
Helen Stephenson's letter, which was accompanied by formal advice on compliance with charity law, says she acted because of "concern about the activities of charities across this sub-sector".
The letter adds: "Ignoring such advice and future breaches of charity law could be deemed as misconduct or mismanagement and will be assessed accordingly."
The letter reminds trustees of existing duties rather than new requirements.
The commission said the report, which was praised by leading Brexit politicians such as Boris Johnson and Jacob Rees-Mogg, "was not sufficiently balanced and neutral as required of an educational charity under charity law" and "overstepped the line of what is permissible charitable activity".
Neil Record, chair of trustees at the IEA, accused the commission of causing confusion and said it was "increasingly unclear what charitable think tank activity is acceptable, and what is not".
Stephenson's letter does not mention any specific charities, but there have been widespread concerns for many years about think tanks pursuing political, party political or propagandist purposes and promoting preconceived views.
The letter says: "Think tanks have an important role in society helping to educate the public.
"Society is richer when it is challenged with new ways of thinking and when debate is stimulated.
"However, think tanks which are charitable must operate and behave as charities."
Asked what prompted the letter, a commission spokeswoman said: "Recent cases have highlighted that trustees of charitable think tanks needed reminding of their legal duties, specifically of what is permissible under charity law for charities that have purposes to advance education and of limitations on campaigning, especially political campaigning by charities."