Want the best of The Telegraph direct to your email and WhatsApp? Sign up to our free twice-daily Front Page newsletter and new audio briefings. Christopher Halliwell was found guilty of murdering Becky Godden (picured) Credit:PA / Wiltshire Police Ahead of his trial for the murder of Miss Godden, Halliwell hinted he would admit to her killing if he were not pursued for other crimes.He told police: “I don’t want to keep coming back every couple of years on different charges.”He added: “If I can clear this up in the next few hours, will everything else be forgotten?”Miss O’Callaghan’s mother, Elaine Pickford, has voiced corncerns that there may have been other murders.Other unsolved cases in areas nearby include Melanie Hall, who disappeared aged 25 in 1996 after leaving a nightclub in Bath; Sally Ann John, a 24-year-old prostitute who went missing from Swindon’s red light district in 1995, and Thi Hai Nguyen a Vietnamese immigrant went missing in Swindon in 2005. Specialist police officers have begun excavation work at the former home of double murderer Christopher Halliwell, it is understood.The 53-year-old taxi driver, of Swindon, Wiltshire, murdered Becky Godden, 20, in January 2003 and Sian O’Callaghan, 22, in March 2011.He was handed a rare full life sentence – meaning he will never be released – at Bristol Crown Court last year after being convicted of Miss Godden’s murder.Following his sentence, police said they were working with other forces and the National Crime Agency to identify potential further victims of Halliwell. Detective Chief Inspector Jeremy Carter, who is leading the investigation, said: “Searches are being conducted in the gardens and garages of two properties in Broad Street over this coming week.”Whilst we do not have plans, at this stage, to search inside the properties there will be some disruption to the occupants.”I would like to make it clear that those living at the addresses have no involvement in the investigation and we thank them for their understanding and patience.”Although we are unable to comment on the nature of our inquiries, we can say that we acting on intelligence received.”Superintendent Charlie Armstrong added: “We understand that this activity may cause concern for the local community and residents can expect to see a police cordon in place within the alleyways in Broad Street for the next five days.”This should not impact upon other local residents. Officers will continue to patrol the vicinity and will be available for anyone who has any concerns relating to the searches.”Halliwell abducted office administrator Miss O’Callaghan as she walked home following a night-out in Swindon and dumped her body in Uffington, Oxfordshire.He then confessed to killing another woman, a prostitute he had picked up from Swindon, had sex with and strangled in January 2003.The father-of-three led police to a field in Eastleach, Gloucestershire, where Miss Godden’s remains were discovered. Detective Superintendent Sean Memory said after Halliwell was found guilty that he was “open-minded” about the possibility of other victims.”I would appeal to Christopher Halliwell, actually, if he wants to speak I’m willing to speak with him,” he said.”He has clearly demonstrated he is very forensically aware. I can’t link him directly to any offences however there is an eight-year gap between the two murders and I have no evidence to suggest Becky was actually the first one.”Wiltshire Police started excavation work based on new information within the gardens of two properties in Swindon town centre on Monday. Work at the addresses in Broad Street is expected to last for five days.