A speeding van was driven into pedestrians on London Bridge, before people were stabbed on the street and in bars in the nearby Borough Market area.
Hundreds of people were in the area when the attacks took place.
BBC reporter Holly Jones was walking across the Bridge when the attack took place.
She narrowly escaped being hit.
"There was a van, a white transit van being driven by a male came speeding towards us and it mounted the pavement and then almost did like a zig zag across the pavement, hit the people in front of me, veered back towards the road and at that point, myself and the person in front jumped out of the way. We were probably less than two metres from being hit by this van, and it then hit the people behind us and it kind of carried on zigzagging down the road and then sped off."
Waiter Alex Martinez was working at the El Pastor restaurant in Borough Market when he says a man ran in carrying a knife.
He told reporters, he hid in a bin.
"I listened to everything when I was inside the bin - the gun, the shooting, the screaming, the crying, the people - but I didn't see nothing."
(Question: "You said you heard guns?") "In the street, the person was shooting. I don't know who, but they were shooting. I listened to the shooting, you know."
Australian Labor Senator Sam Dastyari was in London, where he had earlier met with the city's Mayor, Sadiq Khan.
He told Sky news, he was having dinner near the Borough Market when events unfolded.
"You could hear the screams, you could hear the people running down the street , running past you and one or two of them obviously quite injured. They'd locked down the Borough region. They'd placed the restauranteurs in secure places, and kept us there for about 40-45 minutes and then the police kind of evacuated restaurant by restaurant."
Metropolitan Police Assistant Commissioner Mark Rowley says police initially received a call that a vehicle had struck pedestrians on London Bridge.
He says officers confronted the van's occupants after they moved on to Borough Markets.
"Armed response officers then responded very quickly and bravely and confronted the three male suspects who were shot and killed in Borough Market. The suspects have been confronted and shot by police within eight minutes of the first call. The suspects were wearing what looked like explosive vests but these were later established to be hoaxes."
British Prime Minister Theresa May confirmed the incident was being treated as an act of terrorism.
There's been international condemnation of the attack, with France, Canada and the US among countries that have offered support.
Australian Prime Minister Malcolm Turnbull, enroute from Singapore, tweeted that prayers and resolute solidarity are with the people of Britain in the face of the shocking terrorist attacks.
Opposition Leader Bill Shorten also expressed support for Britain.
"We are united in our resolve to oppose terrorism. It's a moments like this that we throw politics out the window and we're united by determination to keep Australians safe."
No Australians are believed to be involved.
The attack comes ahead of this week's British elections, and less than two weeks after a suicide bomber killed 22 people at a concert in Manchester.
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