The crash happened on the Strand, a busy road that runs through Westminster past universities, hotels and train stations.
Pictures taken at the scene show the road closed by a police cordon near the Strand’s junction with Surrey Street.
Ali, a PhD student at King’s College London, who did not wish to share his surname, was leaving class when he saw emergency services gathered near the scene.
“I was just walking out of class, at first I was disoriented, I thought it was a protest because it usually happens, but it’s something else entirely,” he told our reporter Olivia Carter at the scene.
“(Now knowing a woman has died) is so sad and hard to process – my thoughts go out to her family and friends.
“We walk by that crossing all the time and it’s pedestrianised, barely any vehicles pass.”
The closure runs from Surrey Street to A301 Waterloo Bridge, according to the AA.
The Met Police has confirmed that a woman in her 20s was pronounced dead at the scene following the incident.
Two other pedestrians were taken to hospital – one with potentially life-threatening injuries and the other with minor injuries.
The 26-year-old male driver of the van was arrested at the scene on suspicion of causing death by careless driving and driving with a concentration of a specified controlled drug above the specified limit.
He is in custody while enquiries continue.
A Metropolitan Police statement said: “Police are on scene and dealing with a collision close to The Strand, WC2.
“Officers were called at 11.41am on Tuesday March 18 following a collision involving a van and pedestrians.
“Three pedestrians suffered injuries, with a woman in her twenties sadly pronounced dead at the scene.
“Two pedestrians have been taken to hospital, one has potentially life-threatening injuries, and the other has minor injuries.
“The driver of the van, a 26-year-old man was arrested at the scene on suspicion causing death by careless driving and driving with a concentration of specified controlled drug above specified limit.
“He remains in custody.
“Enquiries are ongoing and a crime scene is in place.
“This collision is not being treated as terrorism-related.”