The officer’s brother, Ronnie Semple, said in a statement that his death had left the world of his family and his partner, Gary, “a worse place”.
Martin Harris, whose brother lives upstairs from the flat where PC Semple’s body was found, confronted the person living at the property about the stench, and said the occupant had put scented candles outside his door to disguise it.
Mr Harris said the door was answered by a man wearing blue Speedo-type swimming trunks and glasses, who was “as cool as a cucumber”.
Mr Harris said: “I asked him what the terrible smell was and he apologised and said he was cooking.”
Still concerned, Mr Harris contacted the police.
Heather Brown, who lives in the block next door to the flat, which police forensic teams are scouring for evidence, said the candles had been outside the door for a “few days”.
Ms Brown said the housing block where PC Semple’s body was found was full of short-let tenants, and described it as a “very quiet place” where there were “never any problems”.
The officer, who had been with the police for 30 years, left his home in Greenhithe, Dartford, to go to work in Westminster last Friday. On the same day, he visited the Shard in Southwark.
He left there at 12:30pm and was last seen on CCTV about two and a half hours later near London Bridge, a short distance from the property where he was found.
In a statement, PC Semple’s brother, Ronnie Semple, said: “On behalf of Gordon’s partner Gary, my wife Maureen, Gordon’s nephew Paul, niece Kerry and I, I would like to thank everyone for their kind thoughts during the past dreadful week. It has been a terrible time for us all, especially Gary.”
He added: “Gordon will be sadly missed by all of his immediate family, his colleagues in the Met Police, former Bank of Scotland colleagues in Inverness and London, friends from his ‘Tartan Army’ days, but most of all the hardest loss is for Gary at this time … Our world will be a worse place without him.”
Officers are continuing a “vital search for evidence” at the scene, Scotland Yard said.
Metropolitan Police Commander Alison Newcomb said: “This is a very sad day for Gordon’s colleagues. There are many officers who have served with Gordon in London during his 30-year career who will acutely feel his loss.”