But a High Court judge later ruled Halliwell's admissions could not be used as Detective Superintendent Steve Fulcher had breached police guidelines on interviewing suspects.
The charge of murdering Miss Godden was withdrawn until March this year following an investigation by Wiltshire Police that uncovered overwhelming evidence against Halliwell.
The 53-year-old former taxi driver had already been convicted of murdering Sian O’Callaghan, 22, in 2011.
After he was convicted of Miss Godden's murder last year, Detective Superintendent Sean Memory said: "He talked candidly in 1985 about wanting to be a serial killer and I genuinely believe that's a distinct possibility." Now officers from Wiltshire Police have begun excavation work across gardens and garages at two properties in Broad Street in Swindon, where Halliwell lived.
Police believe Halliwell abducted Miss Godden from Destiny & Desire, a nightclub in Swindon town centre close to where he took Miss O'Callaghan, in early 2003.
Prosecutor Nicholas Haggan told Bristol Crown Court: "Both were taken in a taxi.
Up to 30 ‘pop-up’ brothels are being opened each week in Swindon, police have said.
In any one week, up to 40 sex workers were marketing their services in properties for a few days before moving on.
Devon and Cornwall Police revealed earlier this year that criminal gangs were using holiday lets in Newquay as brothels.Det Sgt Chris Hitchcock, of Wiltshire Police, said: ‘Many of these women move between addresses within the town as well as outside of it.‘Of these 40, we estimate they populate 20 to 30 brothels in short-term to medium-term rental properties.’He said that officers were looking to ‘intervene and see if we can offer safeguarding, and see if organised crime is involved, as often as we can’.The number of reports of suspected brothels in Swindon nearly doubled between 20, from 60 to 112.Wiltshire Police have said that most of the prostitutes are eastern European and the brothels are understood to be linked to crime gangs which traffic women from Poland and Romania.It is the latest of several locations nationwide, including holiday hotspots in the south West and the Lake District, to be targeted by gangs running ‘transient’ brothels.