Poorna Kaameshwari Sivaraj, 36, and three-year-old Kailash Kuha Raj were discovered at the address in Clayponds Lane, Brentford, shortly before 1am on Tuesday.
Police, who forced entry to the apartment in Golden Mile House, also found a 42-year-old man suffering stab injuries.
He was treated by paramedics but was pronounced dead at the scene.
Scotland Yard later identified him as Kuha Raj Sithamparanathan – Ms Sivaraj's husband and the father of Kailash.
Watch: Triple death tragedy as three-year-old boy and two adults die in west London
Detective Chief Inspector Simon Harding, of the Metropolitan Police said: “Although we are in the infancy of this investigation, it appears that Poorna and Kailash had been dead for some time.
“This is a murder investigation and my team will work diligently to establish the sequence of events that led to their murders and the death of Kuha Raj Sithamparanathan.
“Our initial enquiries have established that Poorna and Kailash had not been seen or heard from for some time, perhaps since around September 21.
He continued: “We know the family often walked their dog, a poodle cross breed, in and around the local area and I would ask anyone who saw them at any time in the last month to contact police so we can begin to build a full picture of their lives.
“I know I speak on behalf of all the officers in my team that words cannot sufficiently sum up the devastation that this horrific incident will have on the families of those involved.
“However, I can reassure them that we will do all we can to provide them with the answers they need about what has happened here.”
Next of kin have been informed of the deaths and post-mortem examinations are scheduled to begin on Thursday.
Met Police commander Peter Gardner said: “This horrific incident has understandably caused enormous shock and concern among local residents and across the borough; all our thoughts are with the family and friends of those affected.
“I would like to thank our officers and paramedics from the LAS (London Ambulance Service) who worked tirelessly and professionally under extremely traumatic circumstances in responding to this incident.
“Our officers in the West Area Command Unit are doing everything they can to support colleagues in Specialist Crime as we work to understand what has led to this terrible incident.
“Local residents can expect to see officers at the scene and patrolling the local area to provide reassurance, and if they have any concerns, I would urge them to speak to our officers.”
Police initially received a call late on Sunday from a family member raising concerns about the welfare of Ms Sivaraj.
Officers attended the address several times in the early hours of Monday but received no reply.
After speaking to neighbours over the course of the day, they decided to force entry.
It is believed that Mr Sithamparanathan fatally injured himself when officers entered the property, the force said.
The Directorate of Professional Standards has made a referral to the Independent Office for Police Conduct over the incident.
Anyone with information that could assist the investigation is asked to contact the incident room on 0208 721 4205 or via 101 quoting CAD7365/6Oct.
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