The grieving husband of Jo Cox, the Labour MP shot and stabbed to death, has called on people to fight “the hatred that killed her” as detectives investigated whether her killing was politically motivated.

The 41-year-old mother of two young children was the victim of a daylight attack outside her West Yorkshire constituency surgery by a man who, according to two witnesses, shouted “Britain first” during the assault.

The first killing of a serving MP since Irish Republicans murdered Ian Gow in 1990 stunned Westminster on Thursday and led to the suspension of campaigning for next week’s EU referendum until Saturday. Cox had taken part in a high-profile event on Wednesday supporting the remain campaign on the river Thames.

Police arrested a 52-year-old man, named locally as Thomas Mair, who was described as using an “old-fashioned” gun and a knife in the attack, shortly before 1pm. Eyewitnesses said Cox’s attacker approached her outside the public library in Birstall when she left her constituency surgery with her aides. In a tussle, he shot her up to three times and stabbed her repeatedly.

The former charity worker and MP for Batley and Spen was declared dead at 1.48pm by a doctor working with a paramedic crew attending to her injuries.

In a statement, her husband Brendan Cox, a former deputy director at Save the Children and adviser to Gordon Brown, said: “She would have wanted two things above all else to happen now. One, that our precious children are bathed in love, and two, that we all unite to fight against the hatred that killed her. Hate doesn’t have a creed, race or religion – it is poisonous.

“Jo believed in a better world and she fought for it every day of her life with an energy and a zest for life that would exhaust most people. “Jo would have no regrets about her life. She lived every day of it to the full.”

Two early lines of inquiry by the police are understood to focus on the suspect’s links to the far right and his mental health. In the hours after the killing, detectives searched Mair’s home for any evidence of extremist rightwing material, held physically or in digital form, as he was referenced on at least one extremist website. Police were checking with the NHS to see if the suspect was known to their mental health services.

Labour’s Stephen Doughty, a friend of Cox’s, said that like many MPs she had faced abuse over a series of issues, including the decision about whether to bomb Syria – on which Cox eventually abstained. “She had a really rough time with a lot of abuse on social media and email,” he said. He said MPs frequently have to report their concerns about threatening behaviour by members of the public to the Fixated Threat Assessment Centre, a joint police-mental health unit which tackles stalking.

A senior Labour source said the party had met Westminster security chiefs repeatedly to call for MPs to be given better protection during their constituency surgeries.

The killing comes six years after 21-year old student Roshonara Choudhry attempted to kill Labour MP Stephen Timms at his advice surgery in Newham, east London. Alan Johnson, the former home secretary, was among MPs who cancelled advice surgeries due to take place on Friday.

Witness Hicham Ben Abdallah said he saw the attacker kicking Cox and then pull a handgun out of a black bag, shooting her and pulling her by the hair. “He was fiddling with the gun, which looked like it was homemade. It seemed like the bullet was lodged, and then he shouted something and began to fire,” he said. “He fired one shot and then three or four seconds later he fired another one. Bang, bang. And that’s when I saw her on the floor in between the two cars.”

Graeme Howard, 38, who lives in nearby Bond Street, said the attacker shouted “Britain first”, adding: “I heard the shot and I ran outside and saw some ladies from the cafe running out with towels. There was loads of screaming and shouting and the police officers showed up. He was shouting ‘Britain first’ when he was doing it and being arrested.”

Another witness, Clarke Rothwell, also told the BBC that Cox’s attacker shouted “Britain first”. He said: “Somebody tried grabbing, wrestling with him, then he was wielding a knife, a hunting knife. He just started lunging at her with a knife, half a dozen times.” He added that people were screaming and running from the area as the gunman started “lunging at everybody with the knife”. A 77-year-old man was also attacked and injured, although not seriously.

The attacker fled down a one-way street as Cox lay dying. Armed police attended the scene and the suspect was eventually pinned to the floor and arrested by local uniformed officers.

The Labour leader, Jeremy Corbyn, said: “The whole of the Labour family, indeed the whole country is in shock and grief at the horrific murder of Jo Cox … [She] died doing her public duty at the heart of our democracy, listening to and representing the people she was elected to serve.”

David Cameron, who cancelled a referendum event in Gibraltar and flew back to London, said: “This is absolutely tragic and dreadful news. We’ve lost a great star. She was a great campaigning MP with huge compassion and a big heart. People are going to be very, very sad at what has happened. My thoughts are with her husband, Brendan, and her two young children.”

The home secretary, Theresa May, said it was entirely appropriate that all campaigning for the referendum had been suspended. “All of us are united in our deep sadness at the loss of one of our brightest and most popular Westminster colleagues,” she said.

George Osborne had been due to use his annual Mansion House speech in the City on Thursday evening to step up warnings about the economic risks of Britain leaving the European Union. Instead, he gave a short statement saying next Thursday’s referendum was “a great exercise in democracy”.

The chancellor said: “People are free in this country to live their lives as they choose and express themselves without fear. Society will protect their right to do so and hold to account those who disregard our laws. Today’s horrible events are an assault on all of these values. But we know that these values, no matter how they have been challenged in the past, have always prevailed, prevail today, and they will always prevail. For they are the values of Great Britain, our great democracy.”

The far-right political party, Britain First, said it was “not involved”. The party’s deputy leader, Jayda Fransen, said she was “extremely shocked” and added: “This is absolutely not the kind of behaviour we would condone.”

On Thursday night, the bishop of Huddersfield, Dr Jonathan Gibbs, led a vigil for Cox. “She grew up here, she lived for this community and in the end she gave her life for this community,” he told the more than 400 people who attended the ceremony at St Peter’s Church in Birstall.

People wiped away tears and embraced each other during the 30-minute ceremony, which was attended by several MPs including Yvette Cooper and Naz Shah. Reverend Paul Knight told those gathered: “We give thanks to Jo for all that she has done for our community. We remember 42 years of Jo’s life as we comfort one another.”

Gibbs added: “She was a woman utterly committed to serving others in the community and making a difference in it and the wider world, and was deeply committed to her own family as a wife and mother.”

Dee Collins, the temporary chief constable of West Yorkshire police, said: “A full investigation is under way to establish the motive of the attack. We are not looking for anyone else in connection with this incident at present.”

Mark Burns Williamson, the police and crime commissioner for West Yorkshire, said: “My thoughts and prayers are with Jo’s family. I am deeply shocked that such a talented young woman has been attacked and killed whilst working in her constituency and serving her community.”

Forensic officers searched Mair’s front garden and garages at the back of the property. Neighbours described the suspect as “a quiet person” and “a loner” who regularly worked on people’s gardens in the area. Mair’s mother said she was too upset to speak.

One neighbour, Emma John, 30, said she saw Mair half an hour before the attack. “I looked out of the window at about 12.30 and he walked past carrying his bag, wearing a cap,” she said. “He looked perfectly calm and normal.” Her mother, Kathleen Cooke, added: “He was a quiet person … we knew him around here from when he used to do our gardens.”

Local teenagers said he he used to shout at them if they congregated on the wall behind his house. Another neighbour said: “All this we are hearing now is totally at odds with the man we thought we knew. We knew him as someone who helped out, who did volunteering.”

The former prime minister Gordon Brown, who knew Cox well, said she was “the most vivacious, personable, dynamic and committed friend you could ever have”, adding: “Our memories will be for ever scarred by this moment. Our hearts will always be hurt at our country’s loss … Whenever you talked to her, the compassion in her eyes and the commitment in her soul shone through. Years of public service advancing the causes she cared passionately about should have been ahead of her.”