Mr Algar, known to friends as Blaise, was found dead at an address in Nowell Road on January 3 after police were called to reports of concern for the occupant.
The 53-year-old man’s dismembered body was discovered at the property, with his arms and legs having been removed.
Emeka Dawuda-Wodu, of no fixed address, was previously charged with perverting the course of justice and appeared at Wimbledon Magistrates’ Court in March.
This week, he was charged by postal requisition with the murder of William Algar. He remains in custody.
Janayo Lucima, 18, from Earls Court, was charged on Monday, 6 January had previously been charged with the murder, though this charge was subsequently discontinued at court and changed to perverting the course of justice.
Two other men, Mark Hardin, 44, from Isleworth, and Simon Emmons, 40, of no fixed address, have both also been charged with perverting the course of justice – with court dates still pending.
Two teenagers remain under investigation, having previously been arrested on suspicion of murder.
A 19-year-old man, was arrested on Friday, 31 January on suspicion of murder and preventing the lawful burial of a body. He has been released under investigation pending further enquiries.
A 17-year-old boy was arrested on Wednesday, 3 June on suspicion of murder. He is released under investigation.
Detectives continue to appeal for information and are especially keen to hear from anyone who may have had contact with William Algar in December 2019.
Anyone with information that could assist police with their enquiries is asked to contact the incident room on 020 8721 4054, or stay anonymous by contacting the charity Crimestoppers on 0800 555 111.