I have just googled "perverting the course of justice" and here is the result: "The course of justice including the police investigation of a possible crime. A false allegation which risks the arrest or wrongful arrest of an innocent person is enough. Pervert also means "alter" and any act that interfers with an investigation or causes it to head in the wrong direction may tend to pervert the course of justice. The Prosecution has to prove that there is a possibility that whatever the suspect has done might lead to a wrongful consequence, such as the arrest of an innocent party."
Martha I note from your post that the BBC website states that the perverting the course of justice relates to the unlawful and concealment of a body. If that is the case then so be it.
I was a member of a Jury when the charge against the defendent was "perverting the course of justice" and the allegation was that he had interfered with a witness in a criminal case. He was found not guilty.
The other time I have heard of this phrase is a woman I was involved with (through my work) whose daughter was driving a car when she purposely drove the car at an enemy and damaged the person. The mother told the police that it was someone else who was driving the car and not her daughter. She was found guilty.
These seem to fit with the google explanation. The trouble is with legal definitions is that they are complex and not always able to be understood by those of us who are not legal professionals.