Emergency services were called to the scene on Churchyard Row in Elephant and Castle, following reports that three people had fallen from a height.
Attempts by emergency responders to resuscitate them were unsuccessful.
The Metropolitan Police said their deaths on Wednesday were being treated as unexpected.
"At 7.29am officers, the London Ambulance Service, London's Air Ambulance and the London Fire Brigade attended a high-rise block of flats on Churchyard Row, Elephant and Castle, following reports that people had fallen from height," police said.
The force added: "At the scene, three people - a man, a woman and a child - were found to have sadly died, despite resuscitation attempts by first responders. Their deaths are currently being treated as unexpected."
Officers said there were no other reported injuries.
Work is under way to formally identify the three people who have died.
Their next-of-kin have been informed and were being supported by specialist officers, police added.
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A London Ambulance Service spokesperson said: "We sent a number of resources to the scene including ambulance crews, a paramedic in a fast response car, an incident response officer and paramedics from our hazardous area response team (Hart).
"We also dispatched a trauma team in a car from London's Air Ambulance.
"Our first paramedic arrived in around four minutes.
"Very sadly, despite the best efforts of our crews, three people were pronounced dead at the scene."
Police have urged any witnesses with information to come forward.
Shanice Brookes, 30, was rushed to hospital after the shooting at roughly 2.45am but was pronounced dead.
South Yorkshire Police previously said Ms Brookes, who worked for a local charity, was shot outside the One Four One bar in West Street and was an "innocent bystander".
The force has now charged two people over her death.
Jemele Rhone, 30, has been charged with murder, possession of a firearm and possession of criminal property.
Deiryen Dyce, 32, has been charged with assisting an offender, possession of ammunition, possession of drugs with intent to supply, possession of drugs and possession of criminal property.
Both will appear at Sheffield Magistrates' Court later on Friday.
A 30-year-old man arrested in Sheffield on Monday on suspicion of murder has now been released and is no longer being treated as a suspect, police said.
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Detective Chief Inspector Andy Knowles from the force said: "Shanice was an entirely innocent bystander who should've been able to enjoy a night out in our city without the fear that she wouldn't come home safely.
"Shanice's family, including her young son, now face the harrowing reality that they will never get to see her again."
DI Knowles added officers are still "appealing for anyone with any information to come forward and speak to us".
Kenneth Law sold the lethal substances across the world, including the UK.
The 60-year-old was facing 14 counts of aiding suicide, all relating to Canadian victims.
He pleaded guilty to aiding suicide charges under an agreement with prosecutors that would see the murder charges withdrawn.
The Canadian national will not be tried in the UK, because prosecutors fear a court may reject his extradition under "double jeopardy" laws - because he will have already been convicted of similar offences in another country.
Specialist Crown Prosecution Service prosecutor Andrew Hudson said including UK victims in the Canadian sentencing process was the "quickest and most effective route" to securing justice.
The National Crime Agency (NCA) and the Crown Prosecution Service (CPS) said 79 UK victims who died as a direct result of purchasing Law's products will form part of the wider case into his offending.
After his Canadian convictions, British prosecutors said Law was a "serial offender who callously exploited many vulnerable and innocent people exchanging their lives for his financial gain".
He sold 1,200 packages to 40 countries from Canada-based websites, with 286 individuals in the UK receiving the products, leading to 112 deaths.
In a letter to bereaved families, the NCA and CPS said it had been established that Law sent 330 products to the UK in total.
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Explaining why the UK victims would be taken into the Canadian case, the letter said: "We recognise that this may be painful to hear, and that some victims and bereaved families may have hoped to see a separate prosecution in England and Wales.
"This difficult decision was reached only after detailed consideration of all available options."
The families of those who died have now called for a public inquiry.
The sister of Aimee Walton, a 21-year-old from Southampton who died in 2022, said "doors have been shut" for families seeking justice.
Adele Zeynep Walton said: "The question for our own country is simpler still - who here will examine how the British state let this happen, and what it will do so that no other family goes through it?
"A foreign sentencing hearing cannot answer that. Only a statutory public inquiry can."
David Parfett, the father of philosophy student Thomas Parfett, who died aged 22 after taking his own life in Sunbury-on-Thames in Surrey, said: "I am angry, but I am not surprised. For months, we have been told that the system is working and that existing measures are enough. They are not.
"If our own country will not put anyone on trial for these deaths, the very least it can do is hold a proper inquiry into how they were allowed to happen."
Law was also investigated by police in the US, Italy, Australia and New Zealand.
Anyone feeling emotionally distressed or suicidal can call Samaritans for help on 116 123 or email jo@samaritans.org in the UK.
Jane Adetoro, 36, Christina Walters, 32, and Rebecca Walters, 31, were recovered from the water in the Sussex city on 13 May.
The inquest into their deaths opened on Friday morning at Brighton and Hove Coroner's Court.
It heard the bodies were recovered shortly before 6am.
Statements detailed how Ms Adetoro and Christina Walters were brought to shore by an RNLI crew and declared dead by a paramedic at the scene.
Rebecca Walters was washed to the shore and also declared deceased.
Senior coroner Penelope Schofield said post-mortems hadn't yet been able to ascertain a provisional cause of death and medical tests were "ongoing".
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However, she said police currently don't believe there was anyone else involved in their deaths.
She told the girls' father, Joseph Jacobson, who was listening remotely, the loss must be "unbearable" and called for social media speculation to end.
The inquest also heard the women had lived together in Greenford, west London, and their occupations were unknown.
Proceeding were adjourned until a full inquest, due to be held on 8 October.
Police have said they've examined hundreds of hours of CCTV to try to piece together the women's last moments.
However, it is still unclear how they ended up in the sea and why they were in Brighton, East Sussex.
The sisters' father said in a previous statement that losing them "has left an emptiness that words cannot heal".
"No words can truly describe the pain of losing three daughters in the prime of their lives," he said
"Jane, Christina, and Becky were more than daughters to me; they were my joy, my strength, and the beautiful light that filled our family with happiness and love."
Ioannis Aidinidis, 46, who lives in Munich, Germany, was charged on Friday with the offence under the National Security Act.
The Metropolitan Police said that the allegations are believed to relate to Iran and the targeting of a UK-based journalist working for Iran International, an independent broadcaster based in London.
Aidinidis was arrested on Saturday in West Sussex by detectives from Counter Terrorism Policing (CTP), and taken to a London police station.
He is due to appear at Westminster Magistrates' Court later on Friday.
There is not believed to be any wider threat to the public in relation to this matter.
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Commander Helen Flanagan, head of CTP London, said: "We know this may cause concern for many people here in the UK, and particularly those working in Persian-language media.
"We continue to work closely with a number of organisations and individuals to provide them with advice and support around their safety and security, and this includes the specific individual and organisation linked to this investigation.
"If anyone has concerns around their safety then they can contact their local police force and further advice and support can be provided."
There is not believed to be any wider threat to the public, police said.