The attempted truck hire failed because Butt failed to provide payment details.
It is thought three victims were killed on the bridge - including one man who was thrown into the Thames - before the attackers left the vehicle and stabbed five people to death around Borough Market.
Eight people were killed in the attack and the three attackers were also shot dead by the police.
London's Metropolitan Police said Saturday that they arrested a 27-year-old man and a 28-year-old man overnight in east London on suspicion of preparing acts of terrorism.
In its most detailed description of the attack yet, the Metropolitan Police said the men had also rented a flat in Barking, east London, to use as a safe house.
Officers searching the house found an English-language copy of the Koran "opened at a page describing martyrdom", as well as bottles "smelling of petrol" and "a bottle of lighter fluid".
And strapped to the trio's waists as they leapt from its doors were fake suicide belts, composed of plastic water bottles wrapped in grey duct tape.
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.
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".
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This is published unedited from the IANS feed. Six minutes later it returned, crossing over the bridge again and making a U-turn at the northern end, the report said.
Instead he resorted to "plan B" and rented a white van which ploughed into pedestrians as the perpetrators launched their rampage last Saturday night, killing eight and injuring dozens more.
Police have arrested 18 people in connection with the attack, five of whom are still in custody.
The massive police probe into the attack continues and by today, 20 arrests have been made and 13 buildings searched.
Police discovered 13 wine bottles containing flammable liquid with rags stuffed in them, essentially Molotov cocktails, and blow torches to ignite them, potentially meant for another wave of attacks.
So far, 282 witnesses from 19 countries have been questioned but police still want more people who saw what happened to come forward.
Scotland Yard said it wanted to hear from anyone renting vans who might have suspicions about a customer.
Met Police confirmed to CNN that Butt was out on bail at the time of the attacks, having been arrested in a low-level fraud offense in October 2016. They decided it was "deeply abhorrent" but not evidence of criminality.
Meanwhile, police are working with "iconic venues" and music festivals to improve their security over the summer.
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