The MI6 spy found dead in a bag three years ago probably locked himself in the holdall and died as a result of a tragic accident, Scotland Yard has said.

Outlining the results of a three-year investigation on Wednesday, the Metropolitan police said Gareth Williams most likely died alone in his flat.

But Detective Assistant Commissioner Martin Hewitt said the police could not "fundamentally and beyond doubt" rule out the possibility that a third party was involved in his death.

Williams's naked body was found in the padlocked bag, with the keys discovered under his body, in the otherwise empty bath in his flat in Pimlico, central London, in August 2010.

Last year, a coroner concluded that Williams was probably unlawfully killed and his death the result of a criminal act. Following an eight-day inquest, the Westminster coroner, Dr Fiona Wilcox, said he was probably either suffocated or poisoned, before a third party locked and placed the bag in the bath.

But Hewitt said Scotland Yard's three-year inquiry had come to a different conclusion and that Williams was "most probably" alone when he died.

"Despite all of this considerable effort, it is still the case that there is insufficient evidence to be definitive on the circumstances that led to Gareth's death," he said.

"Rather, what we are left with is either individual pieces of evidence, or a lack of such evidence, that can logically support one of a number of hypotheses."

Hewitt added that the investigation had added "some clarity and detail" to the case, but that "no evidence has been identified to establish the full circumstances of Gareth's death beyond all reasonable doubt".

A forensic examination of Williams's flat, a security service safe house, has concluded that there was no sign of forced entry or DNA that pointed to a third party present at the time of the spy's death.

Scotland Yard's inquiry also found no evidence of Williams's fingerprints on the padlock of the bag or the rim of the bath, which the coroner last year said supported her assertion of "third-party involvement" in the death. Hewitt said it was theoretically possible for Williams to lower himself into the holdall without touching the rim of the bath.

Winding down the lengthy investigation, which has drawn interviews and statements from 27 of Williams's colleagues in MI6 and GCHQ, Hewitt said the death remained a tragedy that would be kept under review by detectives.

In a statement, Williams's family said they were disappointed with the police findings and that they agreed with the coroner's conclusions that he was most likely killed unlawfully."We are naturally disappointed that it is still not possible to state with certainty how Gareth died and the fact that the circumstances of his death are still unknown adds to our grief," the family said.

"We note that the investigation has been conducted with further interviews upon some of the witnesses who gave evidence at the inquest and that the investigation team were at last able to interview directly members of GCHQ and SIS [MI6].

"We consider that on the basis of the facts at present known the coroner's verdict accurately reflects the circumstances of Gareth's death."

In a press briefing at Scotland Yard, Hewitt admitted it was "a cause of some regret" that the police were not able to definitively explain the circumstances surrounding the 31-year-old's death.

He rejected suggestions that the security services had "pulled the wool" over his eyes, following concerns over how MI6 and counter-terrorism officers had handled some evidence during the initial investigation. It emerged on Wednesday that police only gained access to Williams's spy agency personnel and vetting files after the coroner's inquest ended last May.

Williams, a maths prodigy and fitness enthusiast originally from Anglesey, was a private person with few other close friends aside from his family, police said. In interviews, MI6 and GCHQ colleagues described him as a "conscientious and decent man" and detectives were unable to identify anyone with any animosity towards him or a motive for causing him harm.

As part of the fresh investigation, a forensic sweep of Williams's flat discovered 10 to 15 unidentified traces of DNA, which are being kept under examination, but none on the North Face holdall or around the bath area of the en suite bathroom of the flat's main bedroom. There was also no evidence of a "deep clean" of the flat to wipe all trace of DNA.

Hewitt said: "There are really three hypotheses that you can use here. One is that Gareth, for whatever reason, got himself into that bag and then was unable to get himself out and died as a result of that.

"One is that Gareth, with someone else, got into the bag consensually, then something went wrong and he died as a result of that. The third is that someone murdered Gareth by putting him in that bag. I would argue that any physical absence [of evidence of] a third party being present tends to make the hypotheses that there is a third party present less likely."

He added: "The coroner drew an inference. I am now drawing a different inference."

At the coroner's inquest, two experts tried 400 times to lock themselves into the 32in by 19in holdall without success, with one remarking that even Harry Houdini "would have struggled" to squeeze himself inside. But days after the inquest, footage emerged of a retired army sergeant climbing into the bag and locking it from the inside.

Hewitt said it was now established that it was theoretically possible for a person to climb into the bag and that it was "more probable" that Williams did this before suffocating as a result of the accident. It emerged during the inquest that Williams had an interest in escapology, but the police said it would be speculation to link his death to a failed attempt to escape from the locked holdall.