British Prime Minister David Cameron has written to Australian leader Julia Gillard in support of her planned tax on carbon to combat climate change, describing it as a "bold step", a report said.

The Sun-Herald reported that the Conservative leader had told Gillard the policy would "add momentum to those, in both the developed and developing world, who are serious about dealing with this urgent threat".

"I was delighted to hear of the ambitious package of climate change policy measures you announced on 10 July and wanted to congratulate you on taking this bold step," he wrote, the paper said Sunday.

Labor leader Gillard's plan to impose a tax on the nation's 500 biggest carbon polluters to cut down on harmful emissions has proven divisive in Australia.

While Canberra says the tax will help slow global warming and save natural treasures such as the Great Barrier Reef, critics say it will make not change global emissions but hurt industry, cost jobs and increase the cost of living.

About 1,000 people gathered in central Sydney's Hyde Park on Sunday to call for a fresh election on the issue, saying Gillard had no mandate to introduce the tax in mid-2012 as planned when she was narrowly elected in August 2010.

Gillard has argued that a fixed price on carbon pollution -- or an effective tax -- is the most effective way for the system to work until it switches to an emissions trading scheme in 2015.