Campbell was found dead in a forest in February, after going missing in the East African country's capital, Nairobi.
A manhunt was quickly launched, with police saying there were suspects.
It has now been reported that one of the suspects, Samuel Musembi, has been found stabbed to death after a botched attempt to poison himself.
He was believed to have been in hiding at a friend's house.
On Tuesday, when the friend returned home from work, he discovered the front door was locked. Once he forced his way inside, he discovered Musembi unconscious on the bed.
He was rushed to hospital where he died from his injuries. An autopsy will be carried out to conclude the exact cause of death. Musembi was one of three men wanted for the murder of Campbell.
Kenya's directorate of criminal investigations said it is hunting the men who have “fled and gone into hiding” following the “heinous crime and subsequent dumping of his body”. The directorate named the other suspects as Benard Mbunga Mbusu and Alphonse Munyao Kilewa, alias Edu. They were arrested a year ago for abducting and black-mailing a church pastor.
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Last February, the directorate said Mbusu, Musembi and Kilewa targeted the pastor as he walked to a restaurant in Nairobi. It was claimed they kidnapped and stripped him.
And they were said to have threatened to embarrass him by releasing photographs of him online. Two other people have also been arrested in connection with the crime. Detectives revealed the gang managed to extort 55,000 Kenyan shillings around £330.
The directorate said: “The suspects are linked to the brutal murder of 58-year-old Briton Campbell Scott, whose partially decomposed b...