Witnesses told local media the petite mother of two had been repeatedly shot and stabbed.
A 52-year-old man, named by media as local Thomas Mair, was arrested. Described by neighbours as a loner, there were indications that he had extreme right leanings.
With just six days left before the historic vote, rival groups campaigning for Britain to leave or remain in the European Union ceased campaigning and politicians joined as one to condemn the killing.
But some commentators questioned whether the murder could be linked to a campaign that has stoked high tension by touching on issues of national identity and immigration.
The Times newspaper reported Friday that Cox, who became the first British MP to be murdered since 1990, had "had been harassed in a stream of messages over three months".
Police were considering putting in place additional security, it said, adding there was no known link between the messages and Thursday's attack.
Before Cox's murder, opinion polls were pointing to the likelihood that Britain would vote to leave the EU in the June 23 referendum, a prospect that weighed on financial markets and sent the pound tumbling.
The pound rose with Asian stocks Friday after the previous day's selloff, as investors judged the tragedy increased the likelihood of the "Remain" side prevailing.
- 'White nationalism' -
US advocacy group the Southern Poverty Law Center reported that Mair, who had lived in the area for decades, was a "dedicated supporter" of National Alliance, once the primary neo-Nazi organisation in the United States.
It said he had spent over $620 on reading material from the group, which advocated the creation of an all-white homeland and the eradication of Jewish people.
"Neighbours called him a 'loner' but he also has a long history with white nationalism," the Southern Poverty Law Center said.
It added that Mair had purchased a handbook with instructions on how to make a gun, noting that witnesses told British media the assailant used a gun of "old-fashioned" or "homemade" appearance.
One witness of the attack, cafe owner Clarke Rothwell, told the Press Association that the gunman had shouted "put Britain first" repeatedly during the attack.
"Britain First" is the name of a far-right anti-immigration group, but it denied any involvement.
Dozens gathered outside the Houses of Parliament in a vigil to remember Cox attended by Labour party leader Jeremy Corbyn, flanked by tearful party colleagues.
"What's happened is beyond appalling. We are here in silent memory of her loss," Corbyn said as rain began to fall.
"She was a fearless campaigner, and a voice for the voiceless. We feel shaken," said Fatima Ibrahim, 23, an activist with Avaaz.
In the streets of Birstall, the scene of the attack was cordoned off and police could be seen examining a shoe and a handbag. Mourners left flowers nearby in tribute.
- 'Fight the hatred' -
In the wake of the attack, commentators questioned whether the tone of the EU referendum campaign had stirred up ugly currents.
In the conservative magazine The Spectator, writer Alex Massie noted that the day had begun with the unveiling of a poster by the anti-EU UK Independent Party (UKIP) featuring a queue of migrants and refugees and the words "Breaking point".
"The message was not very subtle: Vote Leave, Britain, or be overrun by brown people," Massie wrote.
"When you present politics as a matter of life and death, as a question of national survival, don't be surprised if someone takes you at your word."
US Secretary of State John Kerry describd the killing as "an assault on everybody who cares about and has faith in democracy".
In Berlin, German Chancellor Angela Merkel said Cox's death was "frightful (and) dramatic" and said her thoughts were with the victim's family.
Cox, whose first speech in parliament defended immigration and diversity, lived with her husband Brendan and their two children aged three and five, on a houseboat on the Thames.
As the news of her death broke, Brendan issued a an impassioned appeal for unity against hatred.
"She would have wanted two things above all else to happen now," he wrote.
"One, that our precious children are bathed in love and two, that we all unite to fight against the hatred that killed her."
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A 52-year-old man, named by media as local Thomas Mair, was arrested. Described by neighbours as a loner, there were indications that he had extreme right leanings.
With just six days left before the historic vote, rival groups campaigning for Britain to leave or remain in the European Union ceased campaigning and politicians joined as one to condemn the killing.
But some commentators questioned whether the murder could be linked to a campaign that has stoked high tension by touching on issues of national identity and immigration.
The Times newspaper reported Friday that Cox, who became the first British MP to be murdered since 1990, had "had been harassed in a stream of messages over three months".
Police were considering putting in place additional security, it said, adding there was no known link between the messages and Thursday's attack.
Before Cox's murder, opinion polls were pointing to the likelihood that Britain would vote to leave the EU in the June 23 referendum, a prospect that weighed on financial markets and sent the pound tumbling.
The pound rose with Asian stocks Friday after the previous day's selloff, as investors judged the tragedy increased the likelihood of the "Remain" side prevailing.
- 'White nationalism' -
US advocacy group the Southern Poverty Law Center reported that Mair, who had lived in the area for decades, was a "dedicated supporter" of National Alliance, once the primary neo-Nazi organisation in the United States.
It said he had spent over $620 on reading material from the group, which advocated the creation of an all-white homeland and the eradication of Jewish people.
"Neighbours called him a 'loner' but he also has a long history with white nationalism," the Southern Poverty Law Center said.
It added that Mair had purchased a handbook with instructions on how to make a gun, noting that witnesses told British media the assailant used a gun of "old-fashioned" or "homemade" appearance.
One witness of the attack, cafe owner Clarke Rothwell, told the Press Association that the gunman had shouted "put Britain first" repeatedly during the attack.
"Britain First" is the name of a far-right anti-immigration group, but it denied any involvement.
Dozens gathered outside the Houses of Parliament in a vigil to remember Cox attended by Labour party leader Jeremy Corbyn, flanked by tearful party colleagues.
"What's happened is beyond appalling. We are here in silent memory of her loss," Corbyn said as rain began to fall.
"She was a fearless campaigner, and a voice for the voiceless. We feel shaken," said Fatima Ibrahim, 23, an activist with Avaaz.
In the streets of Birstall, the scene of the attack was cordoned off and police could be seen examining a shoe and a handbag. Mourners left flowers nearby in tribute.
- 'Fight the hatred' -
In the wake of the attack, commentators questioned whether the tone of the EU referendum campaign had stirred up ugly currents.
In the conservative magazine The Spectator, writer Alex Massie noted that the day had begun with the unveiling of a poster by the anti-EU UK Independent Party (UKIP) featuring a queue of migrants and refugees and the words "Breaking point".
"The message was not very subtle: Vote Leave, Britain, or be overrun by brown people," Massie wrote.
"When you present politics as a matter of life and death, as a question of national survival, don't be surprised if someone takes you at your word."
US Secretary of State John Kerry describd the killing as "an assault on everybody who cares about and has faith in democracy".
In Berlin, German Chancellor Angela Merkel said Cox's death was "frightful (and) dramatic" and said her thoughts were with the victim's family.
Cox, whose first speech in parliament defended immigration and diversity, lived with her husband Brendan and their two children aged three and five, on a houseboat on the Thames.
As the news of her death broke, Brendan issued a an impassioned appeal for unity against hatred.
"She would have wanted two things above all else to happen now," he wrote.
"One, that our precious children are bathed in love and two, that we all unite to fight against the hatred that killed her."
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