The baby was born hours after his mother was stabbed to death in London (Reuters photo)

A baby boy delivered after his heavily pregnant mother was fatally stabbed in London has died.

The boy, named Riley, was delivered in the early hours of Saturday by paramedics after his mother, 26-year-old Kelly Mary Fauvrelle, was found stabbed inside a house in Croydon, south London.

Fauvrelle, who was eight months pregnant, died at the scene. Riley was taken to hospital in a critical condition but died at 0210 GMT on Wednesday.

"This morning, we heard the sad news that Kelly's baby son, Riley, has died in hospital," Detective Chief Inspector Mick Norman said. "Our thoughts remain with their family."

"This tragic development makes it even more important that anyone with information comes forward as a matter of urgency," Norman said.

British police released CCTV footage of a man they wish to trace. He was shown running from Fauvrelle's address shortly before police were called. Two other men arrested on suspicion of murder have been released with no further action.

"We have assured Kelly's family - and I want to assure local residents and the wider public too - that we are doing absolutely everything in our power to find the person responsible," Norman said.

A wave of fatal stabbings in London has been cast as a national emergency by some police officers and politicians, and has prompted a debate about the significant decline in police funding over recent years.

There were 285 fatal stabbings in England and Wales in 2018, the highest level since records began more than 70 years ago.

The Metropolitan Police said there had been 67 reported homicides in London so far in 2019.

The spate of deaths has drawn the attention of the U.S. President Donald Trump and British rapper Stormzy.