Last 16 June, a week before the EU referendum, Jo Cox, MP for Batley and Spen, was murdered by Thomas Mair. The police investigation revealed that Mair had far-right sympathies and had collected materials on Cox, some printed out from the web. Mair was charged with murder, tried last November, and is now serving a whole-life term in HMP Frankland. Investigation into his life disclosed a man without a job, partner or anything resembling a social life. Everyone seems to agree that Mair was a 'lone wolf' killer, whose espousal of a hate-filled ideology drove him to carry out a hateful act in isolation.

But if Mair was such a loner – in this week's BBC documentary on Cox's murder, DS Nick Wallen, who led the investigation for West Yorkshire Police, remarked that Mair's mobile recorded him as having sent three texts in three years – how did he manage to get hold of a lethal weapon, without any criminal background or known underworld contacts? As Wallen said, WYP still have no idea how he came by the sawn-off gun with which he shot Cox (they refused my request to interview them about it). The case came to court, very speedily, with a major hole in the investigation still open.

Mair used a modified .22 Weihrauch bolt-action weapon, commonly used in pest control, which was wrongly described both just after the murder and in some coverage of the trial as 'home made'. It had been stolen, with its barrel still intact, from its legal owner’s 4x4 vehicle in Keighley in August 2015, about ten months before Mair used it to kill Cox. Wallen does not believe that Mair was responsible for the theft of the gun; as he said in the documentary, it probably passed through a number of hands before coming into Mair's possession. Despite this, forensic sweeps of the gun failed to reveal the DNA of any individual known or unknown to police, apart from Mair. That strongly suggests that the gun had been thoroughly cleaned to remove any traces from the hands that it had passed through. Wallen also doesn't think Mair sawed it off himself: no forensic traces exist, for example from his house in Birstall, to indicate that he carried out the modification.

Wallen acknowledges that Mair's profile is far from that of someone who could pick up an illegal firearm at will. So who did he get it from? It's possible that Mair was sought out by the person who gave him the gun, rather than vice versa – perhaps for an ulterior motive, perhaps to do with the referendum, perhaps not. And why aren’t the authorities more interested in finding out? The one person who it's known must know more, Mair, has said nothing since his arrest. I don't know what fills the hole in the story, and neither do you – nor, one assumes, does anyone connected with the official inquiry. But that isn’t a reason not to pose the question.