A local farmer said she called police after seeing the vans blocking a road near the RAF Fairford base in Gloucestershire, as she drove home in the early hours of Sunday.
She said she came across a group of men, some with their faces covered, nearby, and they ran away when they saw her vehicle.
Five British nationals, all in their mid-20s, were subsequently arrested on suspicion of explosives offences and terrorism before being released on bail on Monday.
On Tuesday Trump said he was "disappointed" at the decision by the British authorities to grant the five men bail.
"We were involved in (the investigation), but as you know, your fellow countrymen, let them go," he told reporters.
"Well, they didn't let them go. They put them out on bail. I assume they haven't watched closely … they should not have done that."
It has now emerged that one of the suspects had called the police around an hour before the farmer had reported their activity on Sunday, a development first reported by The Times.
Counter-terror police said on Tuesday that a quantity of petrol but no explosive devices were found in the vans that sparked the security alert near the airbase, which has been used in recent months by US bombers to launch airstrikes against Iran.
Earlier on Tuesday, US Secretary of State Marco Rubio said in a television interview the suspected plot "clearly involves the hand of a foreign actor", but refused to provide further details.
Head of UK counter-terrorism policing assistant commissioner Laurence Taylor said a police response was activated in the early hours of Sunday "due to a range of information that we received".
"We can confirm that no improvised explosive devices have been found. We have found a quantity of an accelerant, petrol, and we have recovered that as part of our investigation," Taylor said outside New Scotland Yard.
The five suspects released on bail "remain under investigation" and "must adhere to very strict conditions".
"I understand why this development was surprising to some, but I would like to reiterate that this is an investigative decision, and one which is grounded in experience and strategy."
Police cordons near the base are expected to be completely lifted on Wednesday, and searches of the London homes of the five suspects are complete.
Speculation over whether Iran had any involvement in the drama, including by tasking proxies to carry out crimes on their behalf on UK soil, remains rife.
Potential involvement by Iran was understood to be one line of inquiry for British investigators, and the nation has used proxies in the past to carry out acts in the UK.
But its London embassy fiercely denied any involvement in the events.
Speaking to Fox News, Rubio said: "It's one that clearly involves the hand of a foreign actor. I won't get into great detail about that yet".
with AP and PA
