Some of the 59-year-old's remains were found dissolving in a bath of acid after police were alerted to the "smell of death" coming from the Peabody Trust Estate in Southwark on April 7.
Brizzi later told officers: "I thought I was getting away with it. All I have left is two buckets' of PC Semple's flesh."
The alleged killer also asked for a shower as "my bath tub has been unusable for days" and told police officers he "just didn't like" his victim.
Other body parts were found in Brizzi's bin and in the communal bins of Peabody Estate in Southwark, where the Italian lived.
One of Gordon's severed feet was found by a member of the public on the south side of the river and attempts were also made to boil the PC's flesh away in pans.
Before the alleged murder, the two men had been trying to persuade other gay men in the area to join them for a "Chemsex" party, the Old Bailey heard.
Only one man agreed to join, but was sent away by Brizzi - who told him over intercom: "We're having a situation here. Someone fell ill but we're taking care of it. So our party is cancelled."
The witness, known only as CD to protect his identity, arrived just after 7pm - thought to be exactly the time Brizzi was strangling his victim.
In the days after the alleged murder, Brizzi bought a haul of hardware including a set of saws, metal sheeting and some large buckets to help him dispose of the body.
Brizzi replied: "People coming and going 1 guy felt bad on G (not that bad) in the end an experience not to be repeated.
"Somehow my address was all over Grindr and people would show up without even bothering [to] text before."
He added: "I did say bring your own chems but apparently is a concept unheard of to any people."
The Grindr user asked him: "Did you have good sex, or were you worrying about the carpet and the ornaments throughout?"
Brizzi replied: "Mostly worried nobody would steal some stuff while I was trying to calm down the dizzy guy on G [GHB]."
At the same time, Brizzi sent a false message on Grindr to Gordon Semple saying: "But this time just 1-1."
Crispin Aylett QC, prosecuting, said: "The defendant appears to have created a cover story in which a number of different people had turned up and one of them (no doubt Gordon Semple) had been taken ill after taking GHB.
"This is not dissimilar to the story the defendant had told CD - 'Someone fell ill but we're taking care of him'.
"At the same time he was giving a false account of what had actually happened, the prosecution suggest the defendant was laying a false trail that was designed to suggest both that Gordon Semple was alive and that their previous encounter had got out of hand in the false way that the defendant had portrayed to this Grindr user."
After a few days, his neighbours started to complain of the overwhelming stench coming from the flat.
The Peabody estate caretaker initially tried to mask the smell with bubblegum scented spray.
When one neighbour knocked on Brizzi's door to complain, the alleged killer answered in nothing but his underpants and a pair of sunglasses.
He responded: "I'm sorry about the smell. I am cooking for a friend."
When officers arrived they were hit by the overpowering stench of cleaning chemicals and rotting meat.
Brizzi was still in his pants when they arrived and officers found the bath full of blue-green liquid with fish-coloured globules floating in it.
The bathroom floor was coated with slime, as well as a number of coloured buckets on the floor and two black bin liners.
Brizzi told them: "I've tried to disolve the body," before adding: "I've killed a police officer."
When he was asked what had happened, he said: "I killed him last week. I met him on Grindr and I killed him. Satan told me to."
The black bin liners were found to contain mounds of flesh, a human pelvis, a hand and part of a spine.
As the two officers continued to explore the flat, Brizzi told them he hadn't eaten all day and began tucking into a bread roll and a carton of milk.
Aylett said: "The officers said that, up until this times, the defendant seemed calm and relatively composed.
"Now, however, he said: 'I spoke to Satan and he was telling me to kill, kill, kill and I agreed at the first opportunity'.
"That led the officer to ask him if he had any problems with his mental health. The defendant said he used a lot of crystal meth but there was nothing apart from that."
Brizzi said he had dumped PC Semple's personal items in a sewer in Bermondsey.
He told them he had put some body parts he had not been able to break down into a bag and taken them to Rotherhithe and dumped them in a quiet place by the river.
He also said the mixture in the bath was Caustic Soda and spirit of salt containing hydrofluoric acid, but that it hadn't been able to dissolve the body.
Aylett said: "He said the chemicals needed to be heated to 300 degrees and he could not get them hot enough.<
"He said that he had put what he described as the 'flabbery' bits in the buckets in the bathroom."
Brizzi told them he had tried to flush the contents of the buckets down the toilet when the police arrived.
He added: "I didn't know who he was. I didn't like him. He just sat on my bed masturbating.
"I was talking online about Satan as a fetish - and crystal meth takes me to Satan. I loved crystal meth and wanted to meet someone who talked about Satan."
PC Semple, from Greenhithe, Dartford, was reported missing by his partner Gary Meeks on Friday 1 April after he failed to come home from work.
The officer, originally from Inverness, Scotland, had worked in banking before joining the Metropolitan Police.
Brizzi, of the Peabody Estate Trust, Southwark, south east London, denies murder.
He admits obstructing the coroner in his duty by dismembering PC Semple's body in order to dispose of it.
The trial, which is expected to last three weeks, continues.
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