A man who beat his girlfriend's five-year-old son to death in a British park because the child had lost a shoe was sentenced to life imprisonment on Tuesday.

Marvyn Iheanacho, 39, from London, was found guilty at Woolwich Crown Courtinfo-icon of the murder of Alex Malcolm.

Witnesses heard a male voice screaming about a lost shoe while a child fearfully apologised on Nov. 20, 2016. The child sustained a deadly brain injury and internal bruising to his stomach, police said.

A post-mortem examination concluded this had been caused by a kick, stamp or punch.

Iheanacho was later seen talking on his phone while a child lay on his back on a bench next to him, a limp arm dangling down.

Rather than taking the boy to a nearby hospital, only five-minutes' walk away, Iheanacho took him home in a taxi, where he attacked the boy's mother, Lilya Breha, when she tried to call an ambulance, police said.

The boy died in hospital two days later. His shoe was found in the park by police shortly after the assault took place.

 "Iheanacho subjected that poor little boy to a brutal assault after flying into an uncontrollable rage just because Alex lost one of his shoes," said Detective Chief Inspector Tony Lynes, of the Metropolitan Police's homicide and major crime command unit.

"Afterwards Iheanacho came up with various stories to try to cover his tracks, insisted his girlfriend lie for him and attacked her when she tried to get medical help for her unconscious son."