While most Melburnians stayed indoors on Monday to keep out of the freezing cold, homeless couple "Kelly" and "John" were told to move their belongings from Enterprize Park.

Melbourne City Council had asked them and others living rough in the area to dismantle their makeshift home on what was the coldest day of the season.

Kelly (not her real name) said she had been begging at her usual spot when someone came and told her about the notice pinned to her tent.

They were given until 5pm to move "all camping equipment" including mattresses and camp stretchers.

Kelly said they were going to move up the road, because they didn't want any trouble. She said it was unfair that the council did not give them more time to shift.

"It is not dignified being homeless. We are ashamed of it," Kelly said. "It is embarrassing and horrifying."

A City of Melbourne spokeswoman said the council had requested that people camping at Enterprize Park area dismantle and remove camping equipment and structures.

The spokeswoman said under council law, camping was prohibited in public places.

"People are not being asked to move on and may continue to use the area in accordance with the law, including to sleep; however there can be no tents, structures and other camping related items within the City of Melbourne," she said.

She said support services had been working with the people sleeping rough in Enterprize Park to "connect them to a pathway out of homelessness".

However, Kelly said she had not seen anyone recently.

The Yarra River Park, across from Crown Casino, is home to a tent city of sorts.

Another temporary resident, David, who has been living in the area for three years, said it was a big camp.

"We need tents to stop the rain getting our shit wet," he said.

"If they don't want us here, they should house us."

On Monday, a red couch and a large mattress took pride of place amid shopping trolleys full of clothes and plastic bags under the railway bridge between Flinders Street and Southern Cross Station.

A table and chair, an upturned milk crate being used as an occasional table, and tents made up the rest of the "community lounge room".

David said up to 14 people used the area, with other visitors dropping in during the day.

He said it would take a long time to pack everything.

"It's too cold," David said.

"If they take our stuff, I'll be spewing."