A date has been set for an inquest into one of WA's most notorious and mysterious cases — the murder of brothel owner Shirley Finn, in 1975.

Ms Finn's body was found slumped in her car by the side of the Kwinana Freeway near the Royal Perth Golf club in South Perth.

She was wearing a full length ball gown and had been shot in the head four times.

The murder was just three days before a tax hearing, at which Ms Finn was threatening to blow the whistle on illicit dealings by politicians, businessmen and police.

Earlier this year Ms Finn's driver Leigh Beswick confirmed long-standing rumours, telling the ABC Finn was in a relationship with then police minister Ray O'Connor, who went on to become WA Premier.

Today, state coroner Ros Fogliani set down a two-week hearing to start on September 11.

Ms Finn's daughter Bridget Shewring, who was only 12 when her mother died, was in the coroner's court for the announcement.

Outside the court Ms Shewring said she had been waiting 40 years for answers about her mother's death was very pleased a date had been set.

Probes failed to find killer

The murder has been one of the state's most enduring mysteries.

At the time, police recovered a bullet cartridge from the back seat of Ms Finn's car but the murder weapon was never found.

Ms Shewring (l), with Ms Wills, says she has been waiting 40 years for answers. ( News Video )

The original police investigation ended after less than a year and two cold case inquiries in 2005 and 2014 failed to find the killer.

Author Juliet Wills said today was an important moment for Ms Finn's family.

"It's been a phenomenal fight for the Finn family," she said outside court.

"They've been hitting brick walls for decades, and for this moment to finally arrive is enormous, and we really hope ... some of the answers that we've been seeking for so long finally emerge in court."

Many of the people involved in the case are dead, but Ms Wills is confident there is still more information to be revealed.

"It's a very dark chapter in WA history and there's a number of authorities that have a lot to answer for. Hopefully now the Finn family can have some of those answers and some acknowledgement for what happened in the past," she said.