The High Court has overturned the right of two brothers to preach without a permit in Rundle Mall in Adelaide.

Samuel and Caleb Corneloup from the Street Church had fought an Adelaide by-law which prohibited preaching, canvassing or haranguing on any road without a permit.

The brothers won an case in the South Australian Supreme Court, which found the law was at odds with the implied constitutional freedom of political communication.

The South Australian Government was joined by the Commonwealth and several states in challenging the ruling in the High Court.

They argued the Full Court erred in holding that the words preach, canvas and harangue in the by-law were inconsistent with the implied constitutional freedom of political communication.

They also said the court erred in assessing the validity of the by-law, by taking into account the possibility council officers administering the permit system may not sufficiently consider the implied freedom when considering whether to grant a permit.

The High Court ruled the by-law was constitutional and the council did have the power to make by-laws for the governance of its area and the convenience, comfort and safety of its inhabitants.

It also found that while the by-law effectively burdened political communication, it did not infringe the implied constitutional freedom.

Won't be silent

Samuel Corneloup expressed his disappointment about the High Court judgment.

"It's obviously disappointing to hear the judges deny freedom of political communication," he said.

"I think it will have ramifications. At the same time, as far as we go, we do have the opportunity to preach and we're going to continue to do so, so we're happy."

Adelaide Lord Mayor Stephen Yarwood said he was pleased with the court result.

"We need to take a good look at the High Court outcome and actually speak to the administration and make sure that we've got our head around this and that we're going to do the right thing going forward," he said.

"We certainly would like to work with the preachers to minimise the impacts on all city users, but also not curtail freedom of speech."

Council CEO Pete Smith said the council wanted to ensure the safety, enjoyment and comfort of shoppers and traders.

"From a council perspective, this case was purely about the legality of our by-laws, not about preaching per se," he said.

"Everyone has the right to free speech, and we are fully supportive of that. We just want to make sure that they exercise that right in a respectful way."

Anna Brown from the Human Rights Law Centre said the High Court had missed a chance to strengthen free speech in Australia.

"It's not to say that free speech is always a trump card but you need to get the balance right and we don't think the council or the High Court in this case has given enough consideration to freedom of expression or the way that laws should or should not impinge upon freedom of expression," she said.

SA Attorney-General John Rau said the cost of the High Court action was still being determined.

"We were put in the awkward position where these people were unrepresented and it was necessary for, in effect, for the state to make it possible for the High Court to even hear this case," he said.

"I haven't yet got a settled final bill but when I do I'm happy to make that public."