By Elisabeth O'Leary and Paul Sandle

BIRSTALL, England (Reuters) - Britain mourned lawmaker Jo Cox on Friday after a man with suspected neo-Nazi links and a history of mental illness was arrested over a killing that has thrown next week's referendum on European Union membership into limbo.

Cox, 41, a supporter of Britain staying in the EU, was shot and stabbed on Thursday by a man who witnesses said shouted "Britain first" in her own electoral district near Leeds in the county of West Yorkshire in northern England.

A 52-year-old man was arrested near the murder scene and police said a firearm was recovered. The man was being questioned on Friday and no charges had been made. British media named the man as Thomas Mair.

Britain First, a far-right nationalist group, denied any links with Mair but a U.S. civil rights group said he had been associated in the past with a neo-Nazi organization.

In Birstall, a quiet town of a few thousand people, weeping mourners laid flowers at a monument near the scene of the attack. One message read: "Fascists feed on fear."

"It is a vile act that has killed her," Jeremy Corbyn, leader of the opposition Labour Party which Cox represented, said as he lay flowers in Birstall with Prime Minister David Cameron on Friday. "We will not allow those people that spread hatred and poison to divide our society."

The killing prompted campaigning to be suspended for the June 23 EU referendum, the tone of which has become ugly and included bitter personal recriminations as well as furious debate of issues such as immigration and the economy.

The murder sent shockwaves around Britain which has strict gun controls and sparked debate about the safety of lawmakers, the heightened tempo of political confrontation and whether the slaying would affect the outcome of the referendum.

Prime Minister David Cameron has agreed to recall parliament on Monday in tribute to Cox, a well-liked mother of two young children and considered an outstanding member of the new intake of Labour parliamentarians. She had been a prominent aid worker.

Both sides have temporarily suspended their national EU campaigns until at least Sunday.

Shares, oil and bond yields rose after campaigning was suspended, reversing earlier losses this week which followed a swing in opinion polls toward the Leave camp.

The implied probability of a vote to remain rose to 67 percent, up from 65 percent on Thursday, according to Betfair odds.

POLICE SEEK MOTIVE

Though the killer's motives were not immediately clear, some investors suggested sympathy for Cox could boost the Remain campaign which opinion polls indicate had fallen behind Leave.

"The motive for the attack remains a key part of the investigation at this time," Russ Foster, Assistant Chief Constable of West Yorkshire Police, said.

The Southern Poverty Law Center (SPLC), a civil rights group based in Alabama, said on its website that it had obtained records showing a Thomas Mair had links with the neo-Nazi organization National Alliance (NA) dating back to 1999.

The SPLC posted images showing what it said were purchase orders for books bought by Mair, whose address is given as Batley in northern England, from the NA's publishing arm National Vanguard Books in May of that year. The orders included a manual on how to build a pistol, it said.

Reuters was unable to verify the report independently.

Mair's brother said Mair had not expressed strong political views, the Guardian newspaper reported.

"He has a history of mental illness but he has had help," the Guardian quoted his brother, Scott Mair, as saying. "My brother is not violent and is not all that political. I don't even know who he votes for."

Neighbors described a man who had lived in the same house for at least 40 years and helped locals weed their flowerbeds and inquired after their pets.

"I'm totally devastated - I didn't want to believe it. He's been very helpful to me. Anything I asked him to do he did very willingly and sometimes without my needing to ask," said next-door neighbor Diana Peters, 65.

"I saw him the day before. I was taking my cats to the vet and he came and asked me how they were," she told Reuters.

Gun ownership is highly restricted in Britain, and attacks of any nature on public figures are rare. The last British lawmaker to have been killed in an attack was Ian Gow, who died after a bomb planted by the Irish Republican Army (IRA) exploded under his car at his home in southern England in 1990.

Britain's Union flag was flying at half-mast over the Houses of Parliament, Queen Elizabeth's London residence Buckingham Palace and Cameron's Downing Street residence.

"UNITE AGAINST HATRED"

The queen wrote a private letter of condolence to Cox's husband. Members of the public and lawmakers, many weeping, laid flowers outside the Houses of Parliament. Beside a picture of Cox smiling, there were dozens of white candles, bunches of flowers and messages of condolence.

"You can't kill democracy," read one message on Parliament Square. Another said: "We will unite against hatred."

Others put flowers on the houseboat on the River Thames where Cox had lived with her husband and two young children aged three and five.

British politicians paid tribute to Cox, a Cambridge University graduate and former charity worker whose job took her to countries such as Afghanistan and Darfur, and expressed shock at the killing, as did leaders across Europe and the world.

Cameron said the killing of Cox, who had worked on U.S. President Barack Obama's 2008 election campaign, was a tragedy.

Hillary Clinton said she was horrified. German Chancellor Angela Merkel called for a more respectful dialogue in political disputes after the tragedy.

Cox had arrived in Birstall for a "surgery" in a library with members of the public, a one-to-one meeting much like when a patient consults a doctor.

In Westminster, where lawmakers do much of their work in parliament, armed police patrol the entrances, corridors and halls but there is often no security in their home electoral districts, or constituencies.

Tempers can flare during surgeries and parliamentarians are often subjected to abuse on social media. Cox had complained to police after receiving "malicious communications" and a man was arrested and later released with a caution in connection with the investigation in March.

A spokeswoman for the House of Commons said it was reissuing security advice to lawmakers and advising them to contact their local police if they had any concerns.

(Additional reporting by Kylie MacLellan, Paul Sandle, Michael Holden, Sarah Young, Andy Bruce, Kate Holton and Elizabeth Piper, Writing by Guy Faulconbridge, Editing by Timothy Heritage and Peter Millership)