On Saturday (April 29) at 6.26pm, a 38-year-old man was arrested in Mulgrave Road, Sutton, on suspicion of the murder of Archie Sheppard.
He was also arrested on suspicion of possession of an offensive weapon, a knife, and remains in custody pending further enquiries.
Police were called by the London Ambulance Service at around 12.10am on Friday April 28 to reports of a man found with stab wounds on a Route 189 bus in Gloucester Place near the junction with Dorset Square.
Officers attended and found 48-year-old Mr Sheppard from Neasden who was pronounced dead at the scene.
His next of kin have been informed.
The police is awaiting an update as to the exact cause of death following a post-mortem, which was due to take place on Saturday April 29.
Detectives continue to appeal for witnesses and information.
They are urgently seeking the public's help in piecing together the events which led to Mr Sheppard's dead.
They continue to appeal for anyone who was in the vicinity of the Brent Cross bus station at around 11pm on Thursday April 28 that boarded the Route 189 bus that left Brent Cross at 11.13pm.
DCI Noel McHugh said: "Whilst we have made an arrest this evening this is just the beginning for my investigation.
"We are now appealing to those who knew Archie Sheppard in whatever capacity to come forward.
"It is important that we establish and get a clearer picture as to who Mr Sheppard was and the lifestyle he was leading, in particular anyone who was with him on Thursday, 27 April and anyone who stayed at his home in Neasden.
"I am also making a fresh appeal for information and witnesses to come forward.
"A number of people have assisted us with our inquiry but there are still a number of witnesses that have yet to come forward and I believe that they could hold vital information that could help with progressing this investigation."
Anyone who witnessed the incident or the events leading up to the murder is asked to contact the incident room on 020 8785 8099 or via Twitter using @MetCC.
Information can also be reported anonymously to Crimestoppers on 0800 555 111 or via the website.
Keep up to date with the latest news in west London via the free getwestlondon app.
You can even set it to receive push notifications for all the breaking news in your area.