Activists behead King George V monument in Melbourne

Melbourne ratepayers will bear the cost of repairing a beheaded monument of King George V, as a statue of Captain Cook that was hacked off at the ankles is restored.

The statue in Kings Domain on Linlithgow Avenue was targeted by anti-colonial activists between Sunday evening and the early hours of the King's Birthday public holiday on Monday.

The holiday marked King Charles III's birthday and was celebrated in Victoria and most other states.

A video posted to social media on Monday showed a person wearing hi-vis clothing and a headlamp using a mechanical saw to hack off the head, which topples and rolls to the ground.

Overlaid with the Sex Pistol's song God Save The Queen, the video shows another person spraying red paint over the statue before writing "The colony will fall" at its foot in a darker shade of red.

The video ends with "Happy birthday motherf***er".

Victoria Police were called after 9am on Monday and are investigating.

Melbourne City Council deputy lord mayor Nicholas Reece said the vandalism was the latest act in a completely vile and reprehensible trend and vowed the statue would be restored.

"The clean up alone is about $10,000 and that's before we get to the cost of repairing and reinstating the statue - this is ratepayers' money we're talking about here," Mr Reece told ABC Radio Melbourne on Tuesday.

"We cannot allow statues to be decapitated or chopped down like this, and that then becomes a trigger for them being removed."

"The red paint, the decapitating - that's an act of violence."

The council will consider adding additional contextual information around the colonisation of Australia to the restored statue and installing CCTV cameras to discourage vandalism.

King George V is the great-grandfather of the current King Charles, who might visit Australia later this year.

Mr Reece mulled how the vandalism, which generated headlines around the world, reflected on Melbourne.

"You can't imagine how he must be feeling seeing his great grandfather being decapitated, and the red paint, which is obviously meant to look like blood," he said.

Port Philip Council vowed to reinstate a statue of Captain Cook at St Kilda's Jacka Boulevard after it was sawn off by the ankles by activists on the eve of January 26.

Mayor Heather Cunsolo on Tuesday confirmed restoration works were now underway with the statue expected to be reinstated by October.

"While there will be no differences to the statue's design, there are several permit conditions which council is working through which will impact the timeline for reinstatement," Ms Cunsolo told AAP.

"These conditions include the requirement to provide contextual information or interpretation alongside the statue."

Port Phillip Council is consulting with Indigenous groups on the contextual information.

Australian Associated Press