Ringleader Khuram Shazad Butt's efforts to hire the bigger truck failed when his payment was declined, the BBC reported.
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 nearly 50.
They tried to hire a seven-and-a-half tonne lorry to carry out their attack but failed to provide payment details and the vehicle was not picked up, prompting them to use a smaller van from a DIY store instead, the report said.
The three terrorists had tied 12 inch (30cm) pink ceramic knives to their wrists and had petrol bombs in the van, it said.
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Butt drove the van into pedestrians on the iconic bridge. He then went on a stabbing spree along with Rachid Redouane, 30, of Moroccan and Libyan descent and Moroccan-Italian Youssef Zaghba, 22, in Borough Market.
The trio were shot dead by the police.
The Metropolitan Police said the men had rented a flat in Barking to use it as a safe house.
Butt hired the van used in the attack from a B&Q store in Romford in the morning of the attack, it said.
On June 3, the van crossed London Bridge heading south. Six minutes later it returned, crossing over the bridge again and making a U-turn at the northern end, the report said.
The attack began with the van driving back along the pavements of the bridge, running down three pedestrians before crashing outside the Barrowboy and Banker pub opposite London Bridge station, it said.
In the back of the white Renault van used in the attack officers found wine bottles filled with a flammable liquid with rags tied to their necks, the report said.
There were blow torches for lighting these "Molotov cocktails". They had added bags of building gravel and several chairs possibly to suggest a reason for having hired the van.
The massive police probe into the attack continues and by today, 20 arrests have been made and 13 buildings searched.
Meanwhile, police said today they have arrested two men linked to the attack on suspicion of preparing terrorists acts after carrying out raids in Ilford and Barking, London.
So far, 282 witnesses from 19 countries have been questioned but police still want more people who saw what happened to come forward.
Police are also appealing for information about the "distinctive" pink "Ernesto" brand knives the men were carrying. They said they had not found evidence of anyone else being involved in the plot - or inspiring the attackers to carry it out.
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