The man arrested soon after yesterday's attack on Jo Cox has been named locally as Tommy Mair.
Speculation about possible motives has focused on his mental health and links to far-right groups.
Several witnesses said they heard the gunman shouting "Britain first" or "put Britain first" during and after the attack, but police are yet to comment on those reports.
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Mair's half-brother, Duane St Louis, said he "had been volunteering at a school for children with disabilities for several years and had never expressed any racist views", The Guardian reports. But the Daily Telegraph says Mair had "a history of mental health problems and had previously subscribed to a far-right magazine".
A January 2006 blog post attributed to the White Rhino Club, a South African pro-apartheid group, mentions him as an early supporter of and subscriber to SA Patriot magazine, says the paper.
The Southern Poverty Law Center, an anti-hate organisation based in the US, has published receipts detailing several purchases made by Mair from National Vanguard Books, the publishing imprint of neo-Nazi group National Alliance.
"The items listed included tracts on explosives and building a homemade gun," says the Wall Street Journal.
In 2010, Mair started volunteering at a local park after learning about the programme through the Pathways day centre for adults with mental health problems, based in nearby Mirfield. He told the Huddersfield Daily Examiner that it had "done me more good than all the psychotherapy and medication in the world".
Police "were poised to put extra security in place" for Cox after a man was cautioned for sending her a stream of harassing messages over three months, says The Times. There is no suggestion that the messages and the attack are linked.
