But details are emerging about a man who has had interests in white supremacy and apartheid.
The 52-year-old is charged in the killing of Jo Cox
, a British member of Parliament described as a fearless campaigner and rising star of the opposition Labour Party. Mair was arrested blocks from the crime scene.
Cox, 41, was shot and stabbed as she emerged from a meeting with her constituents Thursday, a week before an increasingly divisive vote
on whether Britain should cut ties with Europe.
The U.S.-based Southern Poverty Law Center has published
what it says are documents showing Mair has a history of purchasing material from the National Alliance white supremacist organization based in the United States.
The center released
copies of receipts and a 2013 subscription to the National Alliance's publication National Vanguard as well as receipts from 1999 showing purchases for the neo-Nazi book "Ich Kampfe," the "Improvised Munitions Handbook" and other books.
Mair also subscribed to a pro-apartheid group's magazine in the 1980s, the magazine's editor told CNN.
"A Mr. Thomas A. Mair from Batley in Yorkshire subscribed to our magazine S.A. Patriot when we were still published in South Africa itself," A.D. Harvey said, adding the publication had "no further contact with him" after brief correspondence in the mid-1980s.
"We were of course appalled and sickened to learn of the murder yesterday of Ms. Jo Cox," Harvey said.
'A despicable act'
It is too early to know what motivated the attack, which came as Cox campaigned for "Stronger In," a slogan urging the UK to remain in the European Union in next week's referendum.
Cox was an avid campaigner for the rights of refugees and played down fears of immigration, a hot-button issue in the referendum debate.
Police say they are pursuing reports that Mair had ties to right-wing extremists and looking into his mental health after Mair's brother, Scott Mair, reportedly told The Sun newspaper that Mair had a "history of mental illness, but he has had help," and that his brother was neither violent nor political.
"We are aware of the speculation within the media in respect (to) the suspect's link to mental health services and this is a clear line of inquiry which we are pursuing," police said.
Clarke Rothwell, who runs a cafe near where Cox was attacked, told the Press Association that he heard the attacker shouting, "Put Britain first."
Britain First is the name of a UK political party that has been campaigning for Britain to leave the EU.
Thursday, the party's leader, Paul Golding
, denied the group was linked to the attack, calling the act "a downright despicable act of criminality."
"There's no evidence whatsoever that Britain First was shouted, or putting British people first," he said in a lengthy video posted to Facebook.
"The media are acting grossly irresponsible to try and incriminate our organization Britain First in this heinous crime. We had nothing to do with it," he said.
'Very meek and mild'
Diana Peters, a 65-year-old neighbor of Mair's, told CNN there was nothing to indicate such a thing could happen.
"It's a total surprise that he was even capable of thought, let alone action," she said of the long-time neighbor who lived by himself.
"And, yeah, (he's) just an ideal neighbor. Helpful when you wanted it, kept himself to himself," she said, adding he is "very neat and tidy."
Peters lived in the neighborhood when Mair was a child. She moved away but returned four years ago to find he was living in the same house.
She said Mair taught English to foreigners as a part-time volunteer for years.
"Politics never came up in conversation. ... We never talked about anything like that," she said.
She said she never saw anyone visiting his home and had never been inside. But she said she believed Mair visited his mother every Sunday and took her groceries once a week as well.
She described him as a "very meek and mild" man who liked cats.
"He spoke rationally. He did his day-to-day routine," she said.
Peters said Mair has an "immaculate" garden and often tended to neighbors' gardens.
Other neighbors gave similar accounts, saying he was quiet, tidy and often helped with their gardening.
Six years ago, Mair was quoted in the local newspaper regarding his work as a volunteer at Oakwell Hall, a manor house popular with tourists in Birstall.
Mair told The Huddersfield Examiner that voluntary work had "done me more good than all the psychotherapy and medication in the world."
"Many people who suffer from mental illness are socially isolated and disconnected from society, feelings of worthlessness are also common, mainly caused by long-term unemployment," he was quoted as saying.
Mair learned about the volunteering opportunity from the Mirfield-based Pathways Day Centre for adults with mental health problems, according to the paper.
Police cordoned off a house about a 15 minutes' walk from the attack site, which neighbors said belonged to Mair. Officers could be seen coming and going from the property.
'Wouldn't hurt a fly'
West Yorkshire police said they seized a number of weapons, including a firearm, shortly after the attack.
A half brother, Duane St Louis, told ITV News
he'd never seen any sign that Mair had an interest in knives or guns.
Asked whether Mair was racist, St Louis said "no chance." He said Mair had "never been in trouble" and that "he wouldn't hurt a fly," ITV reported.
St. Louis said he last saw Mair three weeks ago. He said he spoke to Mair's mother after the attack and that she was "shocked and can't understand what happened."