The proposal could pave the way for organisations such as Greenpeace to run broadcast ads, which are outlawed by the Communications Act 2003.
In a test case last year, the High Court blocked an attempt by animal rights activists to run TV commercials.
In a report that was published on Wednesday, the Advisory Group on Campaigning and the Voluntary Sector said the ban on non-charitable "social advocacy" groups amounted to "unreasonable stifling" of debate.
Baroness Kennedy, the Labour peer and QC who chairs the group, said: "BP and Tesco can reach millions through the broadcast media, but Amnesty and Greenpeace cannot. Campaigning organisations need to be able to get their messages across. The rules need to change. Campaigning in the 21st century takes place in a minefield of confusion, obstruction and outdated interpretations of the law."