Detective Chief Inspector Simon Harding, of the Met's Homicide and Major Crime Command, said: "This is a tragic case for all of those involved.
"As expected with any incident where someone has lost their life, my officers carried out a thorough investigation into the circumstances of the death.
"We have approached the CPS for early investigative advice, as required under the guidance.
"We have received and considered that advice, and, at present - on the evidence available - we will not seek a charging decision. Therefore, no further action will be taken against the man.
"Whilst there might be various forms of debate about which processes should be used in cases such as this, it was important that the resident was interviewed by officers under the appropriate legislation of the Police and Criminal Evidence Act; not only for the integrity of our investigation but also so that his personal and legal rights were protected.
"There will be an inquest in due course which will further review the circumstances into Mr Vincent's death in a public forum.
"Our thoughts remain with the families whose lives have been devastated by these events."
Police were called in the early hours of Wednesday morning after reports of a burglary in progress and a man injured at an address in Hither Green.
Mr Osborn-Brooks, who was at home with his disabled wife Maureen, had found two men inside the address and a struggle ensued between him and the men.
It is believed that one of the suspects had a screwdriver and threatened the homeowner with it.
Vincent, from Kent, was found collapsed on the street and had suffered a stab wound to the upper body.
He was taken by the London Ambulance Service to a central London hospital where he was pronounced dead at 3.37am.
A post-mortem examination has given a provisional cause of death as a stab wound. Mr Osborn-Brooks suffered bruising to his arms.
He was arrested on suspicion of grievous bodily harm and further arrested on suspicion of murder. He was taken to a south London police before being bailed.
An unnamed cousin of Vincent said on Friday that she was angry the OAP was initially bailed by police.
She insisted he was a "loving person" and the pensioner he fought with should be kept in custody as police investigate him for murder.
The woman told BBC's South East Today: "I don't know what happened in that home but all I know is my cousin is dead today.
"The Henry I know, he was such a loving person and I think it is probably something that just went wrong but he shouldn't have died out of it."
Meanwhile, the second suspect in the burglary fled the scene prior to police arrival and remains outstanding.
On Friday, his house was being boarded up and metal shutters were placed over windows amid security fears
Two vans, one with a cherry picker on the back, arrived this afternoon to secure the empty house.
Heavy duty security grills were also fitted around all the windows. A forensics tent which had been outside the front door was also taken down.
