In his hometown of Sydney, Prime Minister Malcolm Turnbull already faces an image problem. It's almost a year to the day since Peta Credlin dropped the moniker "Mr Harbourside mansion" on the PM, a sobriquet that has irked Turnbull both because it has stuck, and because it is true.

After all, Turnbull's Point Piper pad isn't even your run-of-the-mill mansion. The Turnbulls purchased Le Gai Soleil – "the gay sun" - in 1994 for $5.4 million. It's now worth 10 times that much.

Previous owners include Sydney socialite Klara Saunders, wife of the late Westfield director John Saunders. Another previous owner was a man named Alan Bond, who bought Le Gai Soleil in 1979.

If the prime minister had an image problem in Sydney, the past week has exacerbated his woes in Melbourne.