Three men crashed the vehicle into railings and then ran through Borough Market, randomly stabbing people at bars and restaurants.
Eight people were killed and the three attackers were shot dead by police.
Butt, a 27-year-old Pakistan-born British citizen, 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, were shot dead by armed police eight minutes after the first emergency call.
The truck they had wanted to hire was smaller but similar to the one used in last year's Nice attack in which more than 80 people were killed in France.
But the payment by the gang's leader, Khuram Butt, failed to go through.
Separately, police investigating the London Bridge attack made three arrests in Ilford, also in east London, late Wednesday.
In a rare glimpse into the week-long investigation, police also disclosed a copy of the Koran opened at a page "describing martyrdom" was found at one of the attackers' home.
The statement further explains, "The attackers had wound duct tape around the handles, and in Butt's case, a leather strap had been attached to the handle and was hung around his wrist".
Another arrest was made early Saturday morning in connection with the London Bridge terror attack, just hours after police released additional details about the investigation, including a photo of a knife used by the attackers.
A van mounted the pavement on London Bridge on June 3rd, killing three people.
After his payment was declined, Butt and two accomplices rented the smaller, cheaper van they ploughed into crowds before leaping from the vehicle and lunching a stabbing rampage that left eight people dead and almost 50 injured.
Three French, two Australians, one Canadian, a Spanish and a Briton were killed in the attack.
An ID card for Redouane was also discovered by police. Within minutes, the attackers are shot dead and another police vehicle arrives as people are seen running for their lives.
"We won't let them win and London will carry on", she said.
Haydon said since last Saturday they had taken 262 statements from people from 19 different countries and numerous worldwide inquiries were ongoing relating to the attackers and the victims.
Butt drove the van into pedestrians on the iconic bridge.
Spain's Foreign Ministry says a British autopsy concluded that Ignacio Echeverria, the Spaniard who confronted assailants during last weekend's attacks in London, died after being stabbed in the back.
Only five remain in custody after 13 were released without charge.
She said: "I would suggest to people that London is one of the safest cities on the planet but of course we want you to be vigilant".
"I'm sure there's more witnesses out there - I would appeal for them to come forward".
Security services are set to undertake reviews into intelligence processes and whether they could have prevented the attack.