Victoria’s coroner will not say how long it will take to get results from a second autopsy on Britt Lapthorne.

The 21-year-old’s parents want a second post-mortem examination after they were unhappy about initial autopsy in Croatia, which was inconclusive.

The backpacker’s decomposed body was found in a Dubrovnik cove on October 8 and arrived home on Sunday with Britt’s father Dale and brother Darren.

She had gone missing in the Croatian city on September 18.

Local authorities produced a basic, two-page autopsy report that only described the state of the remains.

It did not determine whether foul play was involved.

State coroner Jennifer Coate today said a post-mortem would be conducted following the “usual process”.

“While we appreciate the intense interest surrounding this story, we are not in a position to provide time frames for the investigation or the completion of tests and subsequent results,” Judge Coate said.

Arriving in Melbourne last night after a harrowing two-day flight from Croatia, Britt’s father Dale vowed never to give up the fight to find out what happened to his daughter.

He feared Croatian police would drop the ball in the absence of the Australian Federal Police, who were due to finish in Dubrovnik at the end of this week.

“While the AFP is there, there will be much more intent on resolving it. If the AFP go, I am concerned that pillar will be taken off,” he said.

A public memorial service will be held for Britt on Wednesday at the Whittlesea City Office, north of Melbourne, followed by a private burial.

Britt’s friend Liza Nas, who helped organise a memorial service attended by 1000 people on Saturday night, said a group of Britt’s school friends will speak at Wednesday’s service.

Ten groups on social networking site Facebook have now been set up in Britt’s memory, with thousands of members and outpourings of grief.

Many of the comments have come from people in Croatia.

A memorial for Britt was also held in London on Sunday.