Metropolitan Police have confirmed they are responding to incidenst in London Bridge, nearby Borough Market, and Vauxhall.
In March, a British terrorist ran down people with a vehicle on Westminster Bridge, killing four, then stabbed a policeman to death outside Parliament.
Another witness called Eric told the BBC he had seen three men come out of a white van after hitting pedestrians and thought they were going to help.
At least 48 patients were taken to five hospitals, London Ambulance Service said, with more than 80 medics having been sent to the scene.
"I just saw loads of people run away from the market and there was people lying on the ground, and there was a taxi driver who rolled his window down and was shouting at people to run", said witness Simon Thompson.
"The recent attacks are not connected, but we believe we are experiencing a new trend in the threat that we face, as terrorism breeds terrorism", May said.
Police said the three men were shot by a police armed response team within eight minutes of receiving the first call at 10:08 pm (0508 in Malaysia).
Addressing media outside Scotland Yard, Ms Dick said: "Last night we saw another appalling and tragic incident in London - something we hoped we would not see again".
"France is doing everything it can to help", the presidency said in a statement, adding that security would be tightened for expatriates voting in London Sunday in the upcoming French parliamentary election. Sky news said police were unable to confirm all attackers were accounted for.
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.
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A stabbing at nearby Vauxhall was unrelated, the Met added.
The Muslim Council of Britain condemned the attack as "cowardly and depraved" and Muslim community leaders have also deplored the Manchester outrage.
"We don't believe there is but we must make absolutely certain ... and as I said we have a very large investigation ongoing and we will be seeking to establish whether anyone else was working with or assisting in any way, or helping in the planning of this attack in the way that you would expect".
The major political parties suspended campaigning in the country's general election for the day, but Prime Minister Theresa May said the vote would take place as scheduled on Thursday, because "violence can never be allowed to disrupt the democratic process".
Grande, who visited victims of the Manchester attack in the hospital on Friday, found herself confronted with another terror attack.
Vowls also saw people pelting the attackers, and said he joined in himself.
May said the men attacked "innocent and unarmed civilians" in Borough Market with blades and knives.
Among the injured in the attack were a British Transport Police officer and an off-duty officer, according to police.
"When I open the door I see three dead people on the floor", he said.
Several witnesses also reported hearing gunshots. After that attack, Britain's official terrorism threat level was raised from "severe" to "critical", meaning an attack may be imminent.
U.S. President Donald J. Trump has voiced his support for the Britain at this time.