Police also released photos of the van the attackers used to mow down people on the bridge.
27-year-old Butt had ganged up with two other accomplices to carry out the terror attack on June 3 that killed eight persons and injured almost 50.
On June 3, the day of the assault, Khuram Butt attempted to rent a 7.5-ton truck online but didn't provide payment details and the rental didn't go ahead, police said. "The effects could have been even worse".
Police have made a number of worldwide inquiries as they work urgently to establish how the three attackers knew each other, as well as investigating whether they were helped through funding or any other means.
The aim of the attackers seems to have been to replicate the attack in Nice, the officer said. It also emerged that multiple petrol bombs were found in the van used, while a copy of the Koran opened at a page "describing martyrdom" was discovered in the east London bolthole where the men plotted the attack. This was the safe house where the attack was planned, police said.
Police believe Butt was driving the van.
The men then drove into pedestrians on the bridge before stabbing people at the nearby Borough Market on the night of June 3.
The trio were shot dead by the police.
In another development, a 27-year-old male suspect has been arrested on Friday (local time) and taken into custody after a warrant was executed on a home in Ilford, Essex.
The three attackers were wearing fake suicide belts consisting of plastic water bottles wrapped in grey duct tape.
"There was no evidence uncovered of any attack-planning in relation to him", Haydon said.
Butt hired the van used in the attack from a B&Q store in Romford in the morning of the attack, it said.
Pictures of the pink-bladed knives which the London Bridge terrorists used to slaughter innocent pedestrians have been released by police.
He is thought to have driven the van, with Redouane and Zaghba in the back.
They stabbed five people who had been enjoying the area's pubs and restaurants.
That evening, he rented a Renault van.
Police also found a number of office chairs, bags of builders' gravel and a suitcase in the van.
"A Saturday night for London, a week after the awful attacks at London Bridge, is a chance for people to show the unity and resilience of this great city and the generosity of Londoners in getting out and raising money to help the survivors, the victims and their families", comedian Amy Lame, appointed London's "night czar" by mayor Sadiq Khan, said.
Police have conducted a series of raids in connection with the attacks and made 18 arrests.
Police have arrested 19 people in connection with the attack.