The Conservatives, Labour, SNP, Liberal Democrats, Greens, and Plaid Cymru have all suspended their general election campaigning in the wake of the tragedy, the BBC reports. Only UKIP have declined to do so, arguing that this is "what the extremists would want."
This morning, Prime Minister Theresa May will chair a meeting of the government's Cobra emergency committee. "Our thoughts are with those who are caught up in these dreadful events," May said in a statement.
Labour leader Jeremy Corbyn condemned the attack as "brutal" in a statement, saying: "Today, we will all grieve for their loss."
The Mayor of London, Sadiq Khan, has released a video statement condemning the attackers as "twisted and cowardly terrorists," and thanking the city's emergency services for their incredible efforts last night.
SNP leader Nicola Sturgeon, Plaid Cymru leader Leanne Wood, and Green Party co-leader Caroline Lucas have also tweeted to offer their condolences.
Prominent figures from the entertainment world have also been sharing reactions on social media. J.K. Rowling celebrated the defiant spirit of the UK's citizens in the wake of last night's attack and the tragedy in Manchester last week.
Naomi Campbell, Helen Mirren, and Cara Delevingne have each responded with Instagram posts.
Today, people are being urged to avoid the London Bridge and Borough Market area while the emergency services continue to deal with the incident.
If you're concerned about friends or relatives who may have been caught up in the attack, you can call the Metropolitan Police's casualty bureau on 0800 096 1233 and 020 7158 0197.