Police believe a body found in an abandoned property in Virginia could be that of Hannah Graham, a British-born university student who has been missing since 13 September.

Officers searching for the 18-year-old University of Virginia student discovered the body in Albemarle county, near to where Graham disappeared in Charlottesville. Forensic tests are being carried out to confirm whether the remains are those of Graham.

Jesse Leroy Matthew Jr has been charged with abduction with intent to sexually assault Graham. Virginia state police say there is a “forensic link” between the 32-year-old and the 2009 unsolved murder of Morgan Harrington, a 20-year-old woman who also went missing from Charlottesville.

Police are also linking Matthew to the disappearance of another Virginia Tech student in 2010, and to a rape in 2012. Matthew was arrested by police in Galveston, Texas, 1,300 miles from where Graham was last seen.

The discovery of human remains could bring to an end widespread searches carried out by thousands of volunteers across Virginia.

Graham, who was born in Reading but moved to the US with her parents at the age of five, was in her second year of study at Virginia Tech, where she was described as a bright student who got top marks in her exams.

Charlottesville police chief Timothy J Longo said officers had spoken to the teenager’s parents shortly after a search team found a body. “Forensic tests need to be conducted to determine the identity of these remains. But we wanted to be quick in informing the Graham family,” he said. “This investigation is complicated, it’s a complex criminal investigation; it is unlikely that we will have any more information in the near future.”

Describing the “unprecedented” search effort, Longo said: “It was 35 days ago since University of Virginia student Hannah Graham disappeared from our downtown pedestrian mall. Thousands of hours have been spent by hundreds of law enforcement and civilian volunteers in an effort to find Hannah.”

Last week Graham’s parents, Sue and John, issued a plea for Virginians to look out for their daughter. Writing a month to the day after their daughter disappeared, they wrote: “It is heartbreaking for us that the person or persons who know where Hannah is have not come forward with that information. It is within their power both to end this nightmare for all, and to relieve the searchers of their arduous task.”

Graham was last seen drinking with a man who witnesses said matched Matthew’s description in Charlottesville on 13 September. Matthew, a nursing assistant, was captured twice on CCTV walking alongside the victim on the same night, police said.

At 1.20am, the 18-year-old sent a text message to a friend saying she had got lost after an evening of drinking and socialising in the town. She was not seen or heard from again. Soon after police released a wanted poster for Matthew and charged him with abduction.

The following day, the suspect’s apartment and vehicle were searched and he was taken into custody. According to police when he was released, he drove away from the police station at high speed, prompting his arrest on charges of reckless driving. By the following Tuesday, investigators said they had gathered enough evidence to charge him with abduction “with intent to defile”, a charge in Virginia that means kidnapping with the motive of sexual assault.

Longo said Matthew’s arrest had also provided a “forensic link” to the case of Morgan Harrington, a Virginia Tech student who went missing from Charlottesville in October 2009. Her body was found three months later on a farm in Albemarle county, a few miles from the discovery of the body believed to be Graham.

Harrington had been at a Metallica concert in Charlottesville, but was separated from her friends and left outside of the arena, where witnesses said she tried to hitch-hike home. Until Matthew was linked to the disappearance, no leads as to who may have taken her had been found.

Harrington’s case has been linked by DNA evidence to the rape of a 2012 woman in Fairfax, Virginia, who survived after a passerby startled her attacker, according to the FBI. Alexandra Topping