The police were called at 6.41 am on Sunday, April 13 after the paramedics of the London ambulance service found a woman with serious injuries in Hatfield Close, SE14.
The officers rushed to the scene along with the London Air Ambulance.
The woman, who believes she was 40, was declared dead in the scene.
Shortly after, at 6.52 AM, a 44 -year -old man entered the Lewisham police station and was arrested under suspicion of murder. He remains in custody.
Police say that man and woman are believed to be known to each other.
Their closest relatives have the informed leg and are being supported by specialized officers.
A post mortem exam will be carried out in due time.
The investigation is installing and urges any person with information to contact the police.
