British security officials said none of the men was considered violent, but they acknowledged the difficulty of predicting whether extremists will turn risky.
Inside the van, gravel, chairs and a red suitcase can be seen, which detectives believe were props for a cover story the terrorists used to justify the rental to their families.
After Butt's payment was declined, the trio of terrorists rented the smaller van that they used to plow into crowds before jumping out of the vehicle and going on a stabbing rampage that left eight people dead and nearly 50 injured.
Saturday's attack - the third in three months in which the majority of the suspects had been on the radar of security officials - has prompted Prime Minister Theresa May to call for tougher counterterrorism laws even if it means changing human rights protections.
Petrol bombs were also found littered alongside the van used to run down victims on London Bridge, suggesting the plot was meant to be more destructive.
Inside, they found 13 apparent Molotov cocktails made from wine bottles and a possible flammable liquid.
"When I come back to Butt trying to get hold of a 7.5 tonne lorry - the effect could have been even worse".
"Many witnesses we've spoken to have provided extremely helpful accounts of the attack", Haydon added, "but we are still missing pieces of the picture".
"The ceramic pink knives were found on or nearby the three attackers - Khuram Shazad Butt, Rachid Redouane and Youssef Zaghba - after police shot them dead at approximately 22.16hrs on Saturday, 3 June", according to a police statement.
The ringleader of the London Bridge terror gang tried to hire a 7.5 tonne lorry hours before the attack, police have revealed.
The office chairs were possibly placed in the van by the attackers to convince friends and family they were in the process of moving furniture. Tape was wrapped around the handles.
Redouane was a chef who also used the name Rachid Elkhdar and police said he claimed to be Moroccan-Libyan.
They believe one of the properties they searched in the east London borough of Barking was the attackers' safe house, where they prepared the attack.
Police have arrested 19 people in connection with the attack. All but five have been released.
Thirteen have been released without charge, while five men aged between 27 and 30 remain in custody. "It looks as if it is pretty much a contained plot involving the three of them, which is supported by the forensic evidence we've got back so far".
Butt, who police consider the attack ringleader, had been on bail after being arrested for fraud in a case in October of previous year, police said. Haydon said police had also received reports of Butt being involved in violent behavior on several occasions, as well as attempting to recruit children for the Islamic State.
While the Islamic State (IS, formerly ISIS/ISIL) has claimed the responsibility for the attack, Haydon said police have so far not found evidence to suggest it was coordinated from overseas, or that the assailants were part of a larger network.
Butt had been warned by police on two occasions - once for fraud in 2008 and once in 2010 for assault.
When asked if the Metropolitan Police needed more resources she said: "We will want more resources to help us and I am sure the same will be being said in the intelligence agencies".
According to the paper, the images were captured near Butt's gym, the Ummah Fitness Centre in Ilford, east London, and show Redouane placing his phone on the floor, before the men move down the road for 10 minutes.
One man arrested on suspicion of drugs and firearms offences was bailed until a date in late June.