Poorna Kaameshwari Sivaraj, 36, and Kailash Kuha Raj, three, were found in Brentford, west London, last Tuesday.
Kuha Raj Sithamparanathan, 42, died from a stab wound to his chest. The case has been referred to the Independent Office for Police Conduct.
Police initially received a call of concern for the the family’s welfare on 4 October.
Officers attended the address several times throughout 5 October but received no reply.
Scotland Yard officers initially received a call late on Sunday from a family member raising concerns about the welfare of Mrs Sivaraj.
They went to the home several times in the following hours but got no reply, and fears heightened after speaking to neighbours on Monday so they forced entry.
The bodies were found at 1am yesterday. Neighbours said the couple, Malaysian-born Tamils who wed in Kuala Lumpur in 2015, were frequently heard arguing.
One local resident, who lives on the sixth floor of their block, said: ‘Things got really bad between them, especially during the lockdown.
‘They are one of the few couples with a young child in our block and you
More neighbours paid tribute to the ‘lovely’ family as they expressed their shock at the news.
One, who gave her name as Jamila and lives in a neighbouring block, told : ‘It’s tragic. They loved their dog and I’d see them all the time taking him out for walks.
‘They were a lovely family. The officers told me that there was blood all over the flat and that the dog had also been killed.’
The Met said from talking to neighbours as the day progressed, concerns heightened and a decision was made to force entry.
Det Ch Insp Simon Harding said: “We now know how this family tragically lost their lives, but we still need to find out why.
“Our initial inquiries established that Poorna and Kailash had not been seen or heard from for some time; Poorna since around Monday, 21 September, and Kailash since around Thursday, 24 September.”
Post-mortem examinations concluded on Friday and found that Mrs Sivaraj died from a knife wound and her son died from compression to the neck.