A 19-year-old man has been arrested on suspicion of attempted murder following a stabbing on board a train near Beckenham junction station.
Officers say a knife has been recovered following a series of inquiries.
Police launched an investigation after a victim in his 20s was taken to hospital with "serious injuries".
The incident took place on board a train traveling to London Victoria shortly before 4pm yesterday.
A 19-year-old man has been arrested on suspicion of attempted murder following a stabbing on board a train towards Beckenham Junction station
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The Met say the victim is in a critical but stable condition and his family are being supported by specialist officers.
An air ambulance was called to the scene after the attack.
In a statement at the time, the British Transport Police said: "At around 3.56pm today (March 27), we received reports of two men fighting while entering a train at Shortlands (railway station).
"A man sustained serious injures consistent with being stabbed.
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“Officers attended, alongside colleagues from the Metropolitan Police Service and the London Ambulance Service, and the victim was taken to hospital with life-threatening injuries."
Officers are continuing to urge witnesses to come forward.
Superintendent Darren Malpas added: “We understand the concerns of the public following this incident and our detectives have been working tirelessly to investigate.
"I hope this arrest will bring some reassurance to those on the rail network.
Officers are continuing to urge witnesses to come forward (stock image)
PA“High-visibility patrols will continue in the area and across the network as a visible reassurance to the travelling public.
“Any witnesses who are yet to get in touch are urged to do so by calling 0800 405040 or texting 61016 quoting reference 397 of 27 March."
A reduced service to and from Beckenham Junction was in place until 8pm last night.