Parishioners, nuns and passers-by rushed to his aid but he was beyond medical help. For some days his identity remained unknown but he was identified from dental records.
For Mr Smurfit, who was 35, it was a terrible end to a life strewn with drunken incidents and stays in psychiatric hospitals - a life in which money brought him no happiness.
A Scotland Yard spokeswoman said police, an ambulance, an air ambulance and the fire brigade attended the incident but could not save the man. She added: "He was taken to the West Middlesex Hospital where he was pronounced dead. His death is not being treated as suspicious."
Fr Anthony Psaila, a curate at the church, said: "It happened so suddenly, nobody was expecting such a thing on a Sunday afternoon. We had baptisms going on, the young people were meeting in the parish centre so there was a fair bit of activity going on and all of a sudden there was screaming and shouting and the whole thing took place."
Fr Psaila added: "The young adults who were there in the centre tried to help him and we put the fire out and all that but the emergency services were immediately on the scene and they were very helpful."
An inquest, which has been opened and adjourned for further investigations, heard that death had been caused by severe burns. The family is arranging for the body to be taken to Ireland.
The dead man was the nephew of Sir Michael Smurfit, billionaire head of a global empire which is based on packaging. Jason was the son of Sir Michael's brother Jeff, one of a number of family members involved in the business.
The actress Victoria Smurfit is a cousin of Jason's who has appeared in the BBC television series Ballykissangel and in films including About a Boy, with Hugh Grant.
Jeff died in 1987, leaving Jason as a wealthy but troubled teenager who has been described as spending his adult life battling with demons. In the years that followed he was in court for being drunk and disorderly, and later banned for drunken driving. In one incident at a golf club a 22-year-old companion drowned after a golf cart fell into an artificial lake.
Jason had homes in the exclusive Dalkey area of Dublin and in London. In the days before his death Jason had flown from Dublin to London, where he was involved in disputes with a taxi-driver and a hotel receptionist. During his last taxi journey he collected two cans at a garage and filled them with petrol.
The taxi then stopped at a church but Jason told the driver to drive on and got out at St Michael and St Martin's church on Bath Road, Hounslow. There he burnt himself to death.
The Smurfits are one of the Irish Republic's best-known business families, often in the news as their enterprise has expanded into countries around the world. Sir Michael is prominent in the horse-racing world and through the prestigious Michael Smurfit School of Business, based in Dublin.
Sir Michael is known for an extravagant lifestyle. He has properties in many counties, a yacht and an extensive art collection. He also owns an upmarket country club in Co Kildare, and is said to drink Chateau Petrus wine.
He regularly appears in the upper reaches of "rich lists". Sometimes described as driven and abrasive, Sir Michael is known for drawing a salary which is in the millions.
The company was founded by Sir Michael's father in 1934 and was later expanded by him and three brothers. Today it is said to employ more than 40,000 people in 20 European companies with other bases in the US, Canada, Latin America, South Africa and elsewhere.