Just four days ahead of the vote, the Conservatives, Labour and the SNP all said on Sunday morning (4 June) they would stop canvassing, with other political parties expected to follow suit.
Ukip refused to suspend its campaigning, however, with party leader Paul Nuttall saying: "This is precisely what the extremists would want us to do".
It comes after at least seven people were killed and more than 48 injured after a van ploughed into pedestrians on London Bridge, with three suspected attackers then going on a knifing spree in nearby Borough Market.
The Met Police, who are treating the incident as a terrorist attack, said all three assailants were shot dead by armed officers.
"The Conservative party will not be campaigning nationally today," a spokesman for the party said on Sunday.
"We will review as the day goes on and as more details of the attack emerge".
A statement from Labour leader Jeremy Corbyn said: "The Labour Party will be suspending national campaigning until this evening, after consultation with other parties, as a mark of respect for those who have died and suffered injury."
The SNP says it too had "suspended all national campaigning in the General Election today".
A spokesperson for the party told the BBC that "no decision has been made" as to whether party leader Nicola Sturgeon would take part in Sunday night's BBC Question Time debate in Edinburgh.
Ukip leader Paul Nuttall refused to suspend campaigning, however.
He said in a statement: "With more people murdered on the streets of our capital city last night by Islamist terrorists, it is more important than ever for us to confront this evil with the democratic principles that have made this country what it is."
He added: "For those of us seeking to serve the people of this country, it is our duty to drive the dialogue on how best to confront and defeat this brand of terrorism. That is what Ukip will be doing today and beyond.
"Therefore, I refuse to suspend campaigning because this is precisely what the extremists would want us to do."
Some on social media called for the general election vote on 8 June to be postponed, with Saturday's incident coming just weeks after parties suspended canvassing when 22 people were killed in the Manchester Arena suicide bombing.
But Corbyn suggested he would not support postponing the vote, commenting: "We will stand together to defend our common values of solidarity, humanity and justice, and will not allow terrorists to derail our democratic process."
Mayor of London Sadiq Khan also rejected suggestions of postponing the general election.
"The general election is taking place on Thursday," he said on Sunday morning. "I'm not an advocate of postponing."
Prime Minister Theresa May is expected to chair a meeting of the emergency COBRA group of top ministers and security officials on Sunday morning.
"This is fast moving investigation," she said. "I want to express my huge gratitude to the police and emergency services who are on the scene. Our thoughts are with those who are caught up in these dreadful events."
Green Party co-leader Jonathan Bartley described the incident as a "brutal, barbaric attack".
"My heart goes out to all the victims and their families," he said. "The emergency services responded in an exemplary fashion and it is clear too that many others responded with selfless bravery and compassion to the awful events in London last night.
"I am sickened that terrorists have again attempted to divide us in such a cruel and crude fashion. They will not succeed. As in Manchester, and in the aftermath of the Westminster attacks, people will come together in the coming days and demonstrate that our way of life is precious and will not be surrendered to those determined to spread fear."
Liberal Democrat leader Tim Farron added: "Tonight's horrific incidents in London remind us how much we owe our emergency services. My thoughts and prayers with everyone affected."