Joseph Reid and Anne Ward, brother and sister of Mary Reid, said their concerns about the investigation had been taken on board by the officers.
Mary Reid’s half-naked body was found on a beach in north Dublin. It was presumed she had either committed suicide or had an accident.
The family has questioned why the scene was not preserved, why no forensic evidence was collected, why the State Pathologist was not alerted and why no attempt was made to trace Ms Reid’s movements on the day of her death.
In an interview with the Irish Examiner last Friday, Mr Reid said it was “more than a possibility” that their sister was murdered.
The Reids met the two most senior officers for the area, Assistant Commission Catherine Clancy and Chief Superintendent Noel White.
“The Reid family believe that this meeting was worthwhile and valuable,” said Mr Reid. He said there would be further dialogue.
“There were no negative aspects to our meeting and (we would like to) express our appreciation to the gardaí for facilitating us by having the meeting in London.”
A post-mortem carried out on Ms Reid found she had drowned, though there were abrasions on her face and above and below the ribcage.
In September 2003, an inquest returned an open verdict after it could not conclude death was by suicide or an accident.