The appeal is aimed at visitors who may have been in London at the time of the attacks and have returned home, or anyone else who may have information. Detectives recovered craft knives from the flat used to cut the leather straps attached to the knives, lighter fluid used in the petrol bombs and other materials linking it directly to the attack.
Haydon said his teams were working flat out: "We also need to watch out for those who may be inspired by these recent attacks".
Mr Haydon said: "When I come back to Butt trying to get hold of a 7.5-tonne lorry - the effect could have been even worse".
Anyone with information can reach police on 0800 789 321 or visit gov.uk/ACT and complete a secure form.
The van was hired by the ringleader, named by police as Khuram Butt.
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.
They are particularly keen to hear from anyone who witnessed the white van targeting individuals on London Bridge, saw the suspects attacking members of the public or armed police engaging the suspects.
There they found an English-language copy of the Koran which had been left open on a page describing martyrdom, along with other items linked to their attack.
Police said the three men - Butt, Rachid Redouane and Youssef Zaghba - had driven up and down London Bridge twice before carrying out the attack, in what appeared as a dry run.
Shortly before 1700 GMT, Butt received a text message confirming his hire of a Renault van instead.
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In the van police found 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.
On June 3, the van crossed London Bridge heading south.
Extra protection against vehicle attacks are now being put on eight London bridges including at Westminster, Waterloo, Lambeth, Tower Bridge, Blackfriars and Vauxhall.
The interior of the van.
Detectives believe the gravel may have been placed in the vehicle to make it heavier, or as part of a cover to justify hiring it, while the chairs may have been used to convince family and friends they were moving furniture.
Haydon also confirmed that the attackers wore fake suicide belts consisting of plastic water bottles.
British police have arrested two more suspects over the London Bridge attack, after revealing that the carnage could have been worse had the attackers succeeded in their goal of renting a truck, rather than a van, to mow down pedestrians.
On Saturday morning, Butt, who Haydon said was believed to be the ringleader, tried to rent a 7.5 tonne truck but did not provided payment details.
He had also been repeatedly reported to police for violent behaviour and trying to recruit young children to Islamic State as well as featuring in the documentary, "The Jihadis Next Door," where he was seen next to a group of men unfurling a black-and-white flag scrawled with Arabic script and associated with the Islamic State group.
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