Brendan McMillan, 27, and Terry McMillan, 58, were stabbed to death at a business on Long Lane in Bermondsey yesterday (July 28).
They were named by Brendan’s rugby club, which shared its condolences on its social media.
Police were called to at about 1pm to a commercial property, where they found and treated four people for stab wounds.
Terry was sadly died at the scene and three other men were taken to hospital.
Terry’s son, Brendan, later died in hospital.
A third man who has not been identified suffering life-threatening injuries.
A 31-year-old man, who is a British citizen and was initially detained in connection with the incident, was arrested the same day.
He remains in hospital and his condition is not life-threatening.
Detective Chief Superintendent Emma Bond, who leads policing for the area, said: “Our thoughts are first and foremost with the family and friends of the victims of this tragic incident.
“Our investigation continues at pace and we are working hard to understand the full circumstances.
“I understand there may be concern in the local community and there will be an increased police presence in the area over the coming days.
“I would also encourage anyone who may be worried to speak to an officer.”
A crime scene remains in place and the investigation continues, the force added.
Police emphasised that the stabbing happened inside a business premises, and that a crime scene is in place at a nearby hotel where the arrested man entered.
Speculation that the man was staying at the hotel is not accurate, the force said.
Anyone with information has been asked to call 101 or report it online.
