Some have even gone as far as to propose banning the use of plastic bags in markets.

So what does the law say? What exactly is the third tier of government allowed to do? And should they be?

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A constitutional brouhaha began last month when two Melbourne councils - Darebin and Yarra - voted to cease Australia Day citizenship ceremonies in support of Indigenous people.

Prime Minister Malcolm Turnbull condemned the decision as deeply disappointing, while Assistant Immigration Minister Alex Hawke stripped both councils of their right to host citizenship ceremonies.

Then Geelong Council used its powers to ban soft drinks from community cafes and canteens. Soft drinks will be phased out across the region over the next two years.

Port Phillip City Council, which runs the popular South Melbourne Market, wants to stop stallholders there handing out single-use plastic bags by the new year.

And a fortnight ago Moreland City Council also voted to drop any reference to Australia Day on January 26, though it will still hold citizenship ceremonies.

Local councils are often told to stick to the three Rs of local government: roads, rates and rubbish.

But the Local Government Act, which establishes councils' purpose, functions and power, is not so specific.

Point 4 in the preamble to the act is crucial here.

The preamble suggests councils are entitled to make decisions that would otherwise be within the realm of state and federal governments.

"It is the role of council to provide governance and leadership for the local community through advocacy, decision-making and action," it reads.

The act goes further: "The preamble and the local government charter are not to be construed as having the effect of limiting the functions and powers of councils under this act, or any other act."

Professor Roberta Ryan, director of the Institute for Public Policy and Governance at Sydney's University of Technology, said since the early 1980s there had been a surge in local councils taking more progressive social views.

She dismissed claims that councils were overstepping the mark and said local government had a history of influencing state and federal government issues, from lobbying for women's right to vote, to pushing for gender equality in the workforce and same-sex marriage.

"Reflecting the views of local communities and advocating their views to other levels of government is actually the fundamental role of local government," Ms Ryan said.

"Councils are much more than just a service provider because they are the level of government closest to the people, so there is a democratic dimension you don't get from any other level of government."

Melbourne University's director of public and international law, Professor Cheryl Saunders, said councils cancelling Australia Day citizenship ceremonies are acting within their legal powers.

She said there was nothing to suggest the federal government could force councils to host them.

"In principle, I would say that there is nothing to stop local government from doing this if that is what they want to do.

"There is certainly nothing in the national constitution that says they can't do it."

The federal government does have one tool to express their displeasure, however: the Citizenship Act, which allows the immigration minister to revoke citizenship powers.

Under a new rule written in the wake of the furore, the mayor or deputy mayor of a local government authority can take a would-be citizen's pledge of commitment, "except" at the City of Yarra or the City of Darebin.

Ms Saunders said arguments that citizenship was not the business of local government appeared to "miss the point".

"If the Commonwealth is using local government to run its citizenship ceremonies, which is obviously a convenient thing for it to do, then [citizenship] is something that is relevant to both the local government and Commonwealth, and potentially the state as an intermediary."

Local governments have acted in the past on social issues which had reached a stalemate on the national level, she said.

Victorian Local Government Association chief executive Kathryn Arndt said contrary to popular belief, councils have never been limited to sticking to roads, rates and rubbish.

"The Local Government Act states the primary objective of councils is to achieve the best outcomes for the local community having regard to the long-term and cumulative effects of decisions," she said.

"The VLGA recognises and supports the powers of councils to carry resolutions, provided it is done within a properly constituted meeting, following community consultation and engagement."