The victims have now be named by police as 62-year-old Albert Alfonso and 71-year-old Paul Longworth.
Paul was British, while Albert was originally from France but later obtained British citizenship.
A 34-year-old man – named as Yostin Andres Mosquera – also from Scotts Road, is due to appear in court later charged with murder.
Mosquera has been pictured alongside the pair at a luxury hotel resort in Cartagena, Colombia (above).
Mosquera was arrested in Bristol during the early hours of Saturday morning.
The force said both victims were known to the man arrested and he had been staying with them at the Scotts Road flat for a short period of time.
“The evidence gathered so far does not suggest there was a homophobic motive in this case, but officers have followed national guidelines and have initially categorised the incident as a hate crime, the force said.
“This classification will assist in shaping elements of the investigation.”
They added this will be reviewed as any clearer evidence of a specific motive becomes available.
They added: “We are making thorough enquiries to establish whether there may be any linked offences in the UK or overseas but so far none have been identified.
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“Detectives will continue to build a full picture of the circumstances, including any previous incident that may be linked in any way to this case.”
It followed a national manhunt, after the bodies of the two men were discovered in suitcases near the Clifton suspension bridge late on Wednesday night.
Mosquera of Scotts Road, west London, was charged with the two counts during the early hours of Monday morning.
The pair continued to live together at a flat in Shepherd’s Bush despite their separation, with Mosquera said to have been staying with them at the Scotts Road address, the Met confirmed.
Mr Longworth was British, while Mr Alfonso was a France national who later obtained British citizenship.
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The Metropolitan Police confirmed they had found further human remains at a flat in Scotts Road, Shepherds Bush in west London after the search was extended following the discovery of the suitcases.
The remains were “sensitively removed” following the discovery, with additional post-mortem examinations also taking place.
Mosquera will appear later today at Wimbledon Magistrates’ Court.
Deputy Assistant Commissioner Andy Valentine said: “My thoughts are first and foremost with Albert and Paul’s loved ones who are coming to terms with this terrible news.
“While we do not believe either of them had any close family, we have identified other next of kin who have been informed and are being supported by specialist officers. We are continuing to try and identify any extended family members.
“I know that this awful incident will cause concern not just among residents in Shepherds Bush but in the wider LGBTQ+ community across London. I hope it will be of some reassurance that whilst enquiries are still ongoing and the investigation is at a relatively early stage, we are not currently looking for anyone else in connection with the two murders.
“Officers have worked with the pan-London LGBTQ+ Independent Advisory Group (IAG) since the identity of the two victims and their sexuality was established. Their advice, expertise and support for the investigation has been extremely valuable
“We will continue to work with them, and with other partners including local IAGs, as the investigation and the policing response continues.”
They confirmed they aren’t looking for anyone else in connection with the murders.
