Within minutes, the attackers are shot dead and another police vehicle arrives as people are seen running for their lives.
The trio used a flat above a bookmakers as a "safe house", leaving behind a copy of the Koran open on a passage about martyrdom.
The discoveries, especially of the plan to hire a truck, suggested more could have been killed.
Butt, 27, and his two accomplices, Rachid Redouane, 30, who claimed to be Moroccan-Libyan, and Youssef Zaghba, a 22-year-old Italian national of Moroccan descent, all died in the attack.
The three, who were not connected to the weekend attack on London Bridge, are being questioned at a south London police station. "How did they know each other?"
"They are told what is happening, why it's taking so long and the goal of us doing what we are doing", said Simpson.
Police also released details saying Khuram Butt, the suspected ringleader of the June 3 attack that killed eight people and wounded 48 more, attempted to rent a larger 7.5-ton truck, but was denied after he failed to provide payment details.
It was not clear why he could not pay, or if he lacked the necessary licence to drive such a vehicle.
Police believe the intended atrocity was on a similar scale to that in Nice, France, in August 2016 when a truck drove into a crowd and left 86 people dead.
In condemning the bloody attacks and remembering the dead, on Monday the Muslim community in London including from Malaysia held a vigil near the London Bridge where the attack started with a van mowing down pedestrians.
Police are now also appealing for information about the pink ceramic knives that were used.
Tape was wrapped around the handles.
Just two days before the United Kingdom election, Prime Minister Theresa May has faced a barrage of criticism for cutting 20,000 officers from police forces in her time as home secretary.
He married a British woman named Charisse O'Leary, who posted on Facebook last month that Redouane was negligent in seeing their young daughter and on one planned visit, she said he told her: "I'm going swimming".
More than a dozen wine bottles filled with flammable liquid and wrapped in rags were found in the van, along with a pair of blow torches.
Earlier, London police admitted that one of the other two attackers, Khuram Shazad Butt, was on their radar as a member of the outlawed radical Islamist group al-Muhajiroun, co-founded by notorious hate preacher Anjem Choudary.
Haydon went on to say that "it's feasible when you look at their actions, they were still fairly close to the van, there is a possibility they could have come back to the van".
Inside the van, gravel, chairs and a red suitcase can be seen, which detectives believe were props for a cover story the terrorists used to justify the rental to their families.
"The problem occurs when we know someone is moving in extremist circles but we don't have evidence to indicate that they are plotting an attack", said the British government official who spoke on condition of anonymity.
The police and other counter-terrorism agencies have come under scrutiny after it emerged that Butt was under investigation when he carried out the attack. He was jailed past year for encouraging support of IS, which has been linked to numerous militant plots in Britain and overseas.
Assistant Commissioner Mark Rowley said an investigation into Butt had been downgraded as there was no evidence he posed an imminent threat.