British MP Jo Cox, who was killed on Thursday, had previously contacted police after receiving "malicious communications" and they had arrested a man in connection with the investigation in March.
Police said that the man that time was not the 52-year-old man who was being held in custody in West Yorkshire following his arrest close to the crime scene.
"Officers received an allegation of malicious communications from Jo Cox MP, and in March 2016 arrested a man in connection with the investigation," police said.
"The man subsequently accepted a police caution."
Cox, a 41-year-old MP in the opposition Labour Party and a vocal advocate of Britain's European Union membership, died after she was shot and stabbed repeatedly by a man who witnesses said shouted "Britain first".
Both sides in Britain's EU referendum suspended campaigning after the attack.
The mother-of-two from the opposition Labour Party, was shot in the face while lying on the ground by a lone attacker in the village of Birstall in northern England, according to witnesses quoted by local media.
Cafe owner Clarke Rothwell told the Press Association the gunman was shouting "put Britain first".
"He shouted it about two or three times. He said it before he shot her and after he shot her," he said.
Cox, who was also reportedly stabbed, is the first British MP to be killed in office since Ian Gow was killed by a car bomb planted by the Irish Republican Army in 1990.
"He shot this lady once and then he shot her again... leant over shot her once more in the face area," Rothwell told the BBC, referring to the attacker.
Previously unreleased photo dated 12/05/15 of Labour MP Jo Cox Source: AAP
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Police said a 52-year-old man had been arrested and a firearm had been recovered from the scene.
Cox, a former aid worker, was only elected to parliament last year but had already made her name campaigning for the government to do more to help Syrian refugees and for Britain to stay in the EU.
Politicians in Britain and around the world paid tribute to her on Twitter:
'My brother is not violent'
The attacker was named by British media as local man Tommy Mair, with neighbours quoted as saying he was a "loner" who kept to himself.
His brother, Scott Mair, told newspaper the Daily Telegraph that Tommy had suffered from mental illness but received treatment.
"I am struggling to believe what has happened. My brother is not violent and is not all that political," Scott Mair said. "He has a history of mental illness, but he has had help."
In the wake of the attack, commentators questioned whether the tone of the EU referendum campaign had been too divisive, pointing in particular to the focus on immigration.
Alex Massie, writing in the Spectator magazine, blamed the "Leave" campaign for raising tensions, saying: "When you encourage rage you cannot then feign surprise when people become enraged".
"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," he wrote.
Asked whether the tense atmosphere around Britain's referendum was a worry, a spokesman for the US State Department emphasised the incident was an "internal matter for the British people".
"We're obviously concerned by the – by this turning – by turning to violence today," spokesman John Kirby added.
After the attack, pro and anti Brexit groups said they were suspending all campaigning for Thursday and Friday ahead of the June 23 EU membership referendum.
Prime Minister David Cameron cancelled a planned rally during a historic but controversial visit to Gibraltar as part of his campaign for Britain to remain in the EU.
Over parliament, the British flag flew at half-mast, while nearby Cox's Labour party colleagues gathered in a vigil for the MP.
"Hatred will never solve problems," party leader Jeremy Corbyn said at the commemoration.
In Birstall, local residents laid flowers near the scene of the attack as police forensic officers were seen examining a shoe and a handbag in a cordoned-off area.
Floral tributes and candles are placed by a picture of slain Labour MP Jo Cox at a vigil in Parliament square in London on June 16, 2016. Source: Getty Images
'EU will survive'
The attack halted a frantic day of campaigning, as two new opinion polls indicated that more Britons now want to leave the EU than want to stay.
If they prove correct, Britain would become the first state in the nearly six-decade history of the bloc to leave.
The looming prospect of a Brexit has sparked volatility in the financial markets and sent the pound plunging, and prompted interventions from a number of EU leaders.
EU President Donald Tusk said: "The EU will survive, I have no doubt".
On a visit to Russia, European Commission chief Jean-Claude Juncker remarked: "I don't think that the European Union will be in danger of death if Britain leaves."
A new survey by Ipsos Mori showed support for leaving the EU now stands at 53 percent compared to 47 percent for those who want to stay in, excluding undecided voters.
Another new poll by Survation put "Leave" ahead by 52-48, excluding undecided voters.
Polling expert John Curtice said the race was now too close to call, telling the BBC: "I think we no longer have a favourite in this referendum."
London's FTSE 100 share index fell 1.1 percent to 5,899, before recovering somewhat to end the day 0.27 percent lower at 5,950.
The pound hit a new two-month low against the euro.
