Cops could be heard ordering: "Stand up, show us your hands".
Seven people were killed and 48 injured in the attack on Saturday, with 21 fighting for their lives in hospital.
Trump said the attack showed it was time to "stop being politically correct and get down to the business of security for our people", after tweeting the night before - as the scenes of panic in London were still unfolding - that it underscored the need for his contested "travel ban" on several Muslim-majority nations.
Witnesses said the terrorists drove into pedestrians on the bridge in the same way as Westminster Bridge attacker Khalid Masood.
Soon after, reports started coming in of stabbings at Borough Market, a nearby area full of bars and restaurants surrounding a popular food market.
Only hours before, bursts of gunfire echoed through the streets - likely from armed police - and at least three blasts rang out as officers performed controlled explosions after sweeping the area for possible bombs.
British Prime Minister Theresa May reacted on Sunday morning by saying things could not continue as they were and that the strategy for dealing with terrorism needed to be reviewed.More news: 12 arrested in east London as May outlines new terrorism strategy
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"We saw injured people on the road, injured people on the pavement", he told Sky News.
Earlier, the High Commission of Canada in the United Kingdom confirmed that a Canadian was "directly impacted" by the attack.
"There are many officers on scene, as we need still to carry out a thorough search of the area to ensure that everyone has been accounted for, and to make the whole area safe", she said.
At another point in the news conference, Khan said he did not want the general elections Thursday postponed as a result of the attacks, and the threat level remained "severe". Major parties including the ruling Conservative party and opposition Labour have agreed to briefly suspend campaigning. Ms.
The prime minister said the election would be held as scheduled. We are an example to the world of a multi-racial, multi-national city. "They were stabbing her", witness Gerard Vowls said. "It looked like the man maybe had been trying to intervene but there wasn't much he could do".
Speaking outside Downing Street, Mrs May said that although there was no direct link between the three incidents: "As terrorism breeds terrorism and perpetrators are inspired to attack, not only on the basis of carefully constructed plots after years of planning and training, and not even as lone attackers radicalised online, but by copying one another and often using the crudest of means of attack". He said he threw chairs, glasses and bottles at the attackers in a bid to stop them. Then two people approached another person and "began to stick the knife in. and then I froze and I didn't know what to do".
It remains to be seen what impact, if any, the London and Manchester attacks will have on the election. Two weeks ago, a suicide bomber blew himself up at an Ariana Grande concert in Manchester, in northwest England, killing 22 people and injuring dozens more.