Fifteen year-old Enrico Sidoli died after being attacked at Parliament Hill Lido in 1976.
He had gone to the busy open-air pool in Hampstead on 8 July with his sister and her children.
Witnesses later told police that Enrico had become involved in an argument with a group of boys before the attack.
It is thought he was thrown into the pool and may have been held underwater before being pulled out unconscious by a lifeguard at around 2.30pm.
Enrico died in hospital on 19 July and a pathologist concluded he died of irreversible brain damage caused by cardiac arrest.
Detectives launched a murder investigation but nobody was arrested or charged. Two men were interviewed under caution in 1976 and 1986 but no further action was taken.
In July 2017 a fresh appeal for information was launched by the Metropolitan Police’s Special Casework Investigation Team.
Two separate £20,000 rewards were offered by the Metropolitan Police and a member of Enrico’s family.
Police are also trying to identify a potential key witness captured in a photo taken while Enrico was being resuscitated at the side of the pool.
DI Susan Stansfield, of the Met’s Special Casework Investigation Team said: “This tragic incident happened on a hot summer’s day, and there were hundreds of schoolchildren and families at the pool.
“Investigators at the time spoke to dozens of witnesses. We believe that there are others who saw what happened and have vital information that could assist us. Detectives’ efforts to find out what happened that day have been hampered by a lack of information from reliable witnesses.
“We would urge anyone who was at the pool that day and has information relating to Enrico’s death to do the right thing and come forward and help us with our investigation. Your information could unlock this case and give Enrico’s family some answers.
“A picture was taken just after Enrico was rescued from the water, and it shows a dark-haired man swimming in the pool. He has never been traced or spoken to by police, and we would be very interested to talk to him about what he saw that day.
“I hope that after 41 years, any witnesses who were too scared of, or had loyalties to, the people involved at the time will now find the courage to contact police.”
Elizabeth Brown, Enrico’s sister, said: “Enrico was attacked and left for dead at the Lido. He was in hospital for eleven days in intensive care and we, his family, waited, hoping and praying that Enrico would pull through. He died on 19 July 1976. He was only 15.
“On that day it was as if the light went out of our mother’s life. She was consumed by grief, pain and despair. Enrico was her eldest son and the light of her life, and to have been stolen from her so cruelly was unbearable.
“Enrico’s father and all of us, her other children, were unable to console her as we were also in shock and numb with grief. No family should go through this ordeal.
“Enrico’s mother died of a broken heart. Her only wish was to know who did this to her son, and why. Enrico’s father died also asking the same question. We, his brother and sisters, have lived with this dark shadow over our lives for over 40 years.
“Time has passed but the pain has not diminished. We have never stopped loving or missing our brother, we desperately need your help so that this question can be answered and Enrico can have the justice he deserved.
“Please help us find those responsible for Enrico’s death. Please, if you know anything, come forward.”
Iolanda Sidoli, Enrico’s sister said: “I was 13 when we lost Enrico. The pain of losing him has never gone. I remember crying uncontrollably. I was a child whose heart was broken and have never really recovered from the loss.
“When Enrico died, we all died. Our mother and father suffered terribly. Our mother never recovering from his terrible death, spending days and nights by his grave. But the worse thing is how Enrico must have suffered at the hands of the cruel people who took his life.
“He couldn’t swim. I think how frightened he was, with no-one there to help him. If it was you who committed this terrible act towards an innocent kind young boy, then I think the time has come for you to come forward.
“Maybe you have children, even grandchildren. Is this playing on your mind? What you did didn’t just end Enrico’s life; it ended his entire family’s lives. How can you live with this? It must be eating you away inside. Are you suffering like we are suffering?
“My whole life and that of my family was ruined the day Enrico died, and that was because of you.”
If you were at Parliament Hill Lido and saw what happened to Enrico on 8 July 1976, or if you have any information that could assist police with their enquiries, you can call the Met’s Specialist Case Investigation Team on 020 7230 7963. Alternatively, call Crimestoppers anonymously on 0800 555 111.