There they found evidence that linked it to the attack and an English-language copy of the Koran, open at a page describing martyrdom, said Commander Haydon.
The married father-of-three said the incident was the worst he has seen in 18 years as a policeman.
Dozens of people were also injured in the attack, which began shortly before 22:00 BST.
British police said Saturday that Butt, the ringleader, tried to rent a 7.5-ton truck online on the morning of June 3, but did not provide payment details when prompted.
Mr Cole found wounded lying on the ground when he arrived at Borough Market minutes later.
"We had some updates on the radio about at least three men attacking people with knives, but it wasn't really a clear situation and we were not really sure what to expect", he said.
"I then heard more shouting and a stream of people came out of the market screaming and panicking".
A week after the attack, many people on Saturday paused by the sea of flowers as pubs metres away were busy again. Top row left to right: Alexandre Pigeard, Christine Archibald, Ignacio Echevarria, Sara Zelenak.
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Commenting on the impression he is getting from customers, he said: "It hasn't been forgotten, but I don't think it's going to push them into a corner where they're not going to go out". "It was a nice touch".
"I have not seen this tactic in the United Kingdom before where terrorists create maximum fear by strapping fake explosives to themselves".
Cole, 41, said the attack was "the most challenging, most intense situation I've dealt with" in an 18-year police career.
"I went down into the basement - there was probably 200 frightened people there, all waiting to find out what happened".
The business editor of the Sunday Express, who was stabbed during the attack, has written about his ordeal for his newspaper, whilst recovering in hospital.
Writing in the newspaper, he described the moment three potential suicide bombers broke through a locked door.
Meanwhile, it has emerged that Government guidance issued days after the attack warns hospitals and doctors surgeries that they too could be targeted by terrorists. "I had to delay them, stall them any way I could. What they did encourages me". With the help of his friend, he managed to create makeshift bandages to stem the bleeding. They were shot dead soon after by police.
Asked what she thought the lively atmosphere of revellers enjoying their Saturday night said about London, the 27-year-old said: "It is one of the best cities in the world".
"Those guys are the real heroes".