This would cover campaigning to change the law or government policy in furtherance of charitable objectives, but would not alter the bans on political organisations becoming charities and charities providing across-the-board support for political parties.
The group wants the measure to be included in the constitutional reform bill expected in the Queen's Speech on 6 November. It will be meeting Ed Miliband, Minister for the Cabinet Office, and lobbying for the bill to be used to amend the Charities Act 2006 so political campaigning is allowed under the public benefit test.
Rules on political campaigning are currently set out by the Charity Commission in its guidance document CC9, which is based on case law. It says political campaigning must not become a "dominant" activity and must "remain incidental or ancillary to the charity's purposes".
The commission is revising the guidance after pressure from charities, the Advisory Group on Campaigning and the Voluntary Sector, chaired by Baroness Helena Kennedy QC, and the Government (Third Sector, 26 September).
In July's Third Sector Review, the Government said it saw no objection to charities pursuing their purposes wholly or mainly through political activities, provided those purposes were demonstrably charitable.
At a meeting of the regulator's board on 26 September, the commissioners agreed to drop the "dominant/ancillary" rule. But the coalition, which is made up of organisations that contributed to the advisory group, including environmental charity People and Planet, the umbrella bodies Acevo and the NCVO, and Oxfam, argues that the move does not go far enough.
Rosamund McCarthy, a partner at law firm Bates Wells and Braithwaite and a coalition member, said: "We always said piecemeal reform wasn't enough - we want a statutory clarification. Some of the case law on campaigning dates back to 1947. Society has moved on.
"The amendment would have to be drafted very carefully so it doesn't have any unintended consequences. But we feel that if charities can engage 100 per cent in service delivery, they should also be able to engage 100 per cent in campaigning."
Greg Clark, the Conservatives' charities spokesman, said the amendment would be a mistake. He said: "This will have a detrimental effect on public trust in charities and could open the door to political parties becoming registered charities."
McCarthy said: "Charities should not become party political, and the amendment would guard against that. Donors are more sophisticated: if they disapprove of what a charity does, they will stop giving to it."