LONDON—As Britain reeled from the killing of 41-year-old Labour Party lawmaker Jo Cox, authorities were focusing on one thing in particular: determining her attacker’s motive.

Ms. Cox died after a man carrying a gun and a knife launched a bloody daylight attack on her in a street in northern England on Thursday, authorities and witnesses said.

The killing prompted a temporary halt to official campaigning ahead of the referendum on the U.K.’s European Union membership, throwing the issue into limbo a week before the June 23 vote.

Police said they had arrested a 52-year-old man in connection with the attack, had recovered some weapons including a firearm, and were investigating his motive.

They declined to identify the suspect, but local media reports identified him as Thomas Mair. Neighbors confirmed that the house a police forensic team was searching was Mr. Mair’s, adding that he had worked as a volunteer gardener and described him as a reclusive man. A local newspaper story from 2010 quoted Mr. Mair as saying he suffered from mental illness.

The Southern Poverty Law Center, a U.S. nonprofit that tracks extremist groups, said Thursday night that it had obtained invoices with Mr. Mair’s name and address showing purchases dating back to 1999 from the publishing arm of an American neo-Nazi group called the National Alliance. The items listed included tracts on explosives and building a homemade gun.

The documents, posted on the center’s website, couldn’t be independently verified.

One witness to the attack, Hichem Ben-Abdallah, described seeing the alleged perpetrator with what he said resembled “a sawn-off shotgun or something homemade.”

Heidi Beirich, a director at the SPLC, which has long tracked the National Alliance and similar groups, said the center generally receives internal documents from disgruntled former members. Facing legal problems, the National Alliance fell apart about a decade ago, according to the SPLC.

“Our working presumption is that this is a lone incident,” said West Yorkshire police Chief Constable Dee Collins.

The attack occurred shortly before 1 p.m. on Market Street in Birstall, near Leeds in the lawmaker’s West Yorkshire constituency, police said. A 77-year-old man also suffered injuries, but they weren’t life-threatening.

Witness Clarke Rothwell said he had seen the attacker shoot Ms. Cox and that he had also seen him stab her “four or five times.” In a text-message exchange with The Wall Street Journal, he also said he had heard the attacker say “Britain first” and then repeated something similar.

In an interview with the British Broadcasting Corp. Mr. Rothwell said he had heard a loud noise behind him and that as he turned around to look he saw a man bent over a woman with what looked like a gun in his hand. The attacker, he said, shot her as she tried to crawl away, then wielded a knife at others who were trying to subdue him.

Kate Greene, a 33-year-old mother who lives with her husband and three young children in a house that shares a wall with the suspect’s two-story home, said he spent hours a day tending to his backyard garden. He always wore gloves and he used a tissue to open his garden gate, she said.

She said the last time she saw him was on Thursday, as she got off a bus in the commercial district at 12:50 p.m., shortly after the attack. “He looked absolutely fine,” she said.

Born and raised in West Yorkshire, Ms. Cox worked in the aid-agency and charity sector before being elected to Parliament last year, according to her website.

Ms. Cox had studied at Cambridge University, becoming the first in her family to graduate from college, according to her website. Before entering politics, she spent a decade working for the aid agency Oxfam and later worked at the Bill and Melinda Gates Foundation and the Freedom Fund, a charity working to end modern slavery.

In Parliament, she pushed for more robust international action to help Syrians who had been caught up in fighting there, colleagues said. More recently, she was a vocal proponent of Britain remaining in the EU.

In a post on her official Twitter account Wednesday, Ms. Cox put up a photograph of what she said was her husband and children on a boat on the Thames River holding a campaign flag emblazoned with “In” paired with the message “because we’re #StrongerIn.”

Both official groups in the EU referendum campaign—Britain Stronger in Europe and Vote Leave—said they had suspended campaigning activities for Thursday and Friday.

Financial markets, which for the better part of a week have been moving sharply up and down on news from Britain, appeared to interpret the killing as an event that could shift voter sentiment toward the remain camp.

In betting markets, the odds of a remain vote climbed Thursday. A poll showing a six-point edge for the leave camp had pulled the chances of a remain vote down to 57.8% around midday, according to Betfair data reported by PoliticalOdds.bet. At 5 p.m., they had risen to 63.7%.

Ms. Cox’s murder came amid a campaign that is close, hard-fought and angry, but those tensions took a back seat Thursday.

“This is absolutely tragic and dreadful news and my thoughts are with Jo’s husband, Brendan, their two children and wider family,” said Prime Minister David Cameron. “We’ve lost a great star. She had a big heart and people are going to be very, very sad at what has happened.”

“It’s right that we are suspending campaigning activity in this referendum and everyone’s thoughts will be with Jo’s family and her constituents at this terrible time,” added Mr. Cameron, who had been scheduled to hold a rally in Gibraltar Thursday in favor of the U.K.’s continued membership in the EU. He called off the speech

Jeremy Corbyn, the leader of the Labour Party, said the party and the whole country will be in shock at Ms. Cox’s “horrific murder.”

“Jo died doing her public duty at the heart of our democracy, listening to and representing the people she was elected to serve,” Mr. Corbyn said.

“It is senseless that her life should be cut short in such a brutal manner,” said Will Straw, executive director of Britain Stronger In Europe. “This tragedy has shocked everyone in the campaign and especially those in Yorkshire who had been working with her,” said Mr. Straw, describing Ms. Cox as a good friend.

Her husband, Brendan Cox, said in a statement reported by local news media that she had “a zest for life that would exhaust most people” and said her friends and family would “fight against the hate that killed Jo.”

“Today is the beginning of a new chapter in our lives. More difficult, more painful, less joyful, less full of love,” he said.

Violent attacks on lawmakers in the U.K. are rare, but not unheard of. In May 2010, a young woman attacked then-Treasury minister and Labour lawmaker Stephen Timms with a knife. A jury later that year found British-born Roshonara Choudhry guilty of attempted murder.

Prosecutors said she was influenced by Anwar al-Awlaki, the U.S.-born radical cleric connected to a Yemen-based affiliate of al Qaeda. Mr. Timms was hospitalized for a week before recovering.