Ronnie Barker's son Adam could be arrested if he attends his father's funeral after he skipped bail while facing a child porn inquiry last year.
The entertainment world has paid tribute to Ronnie Barker
Mr Barker, 37, went missing after being arrested in June during a crackdown on child porn accessed via the internet.
The actor, from west London, appeared in ITV detective series Wycliffe. He is believed to have fled overseas.
Ronnie Barker, 76, star of Porridge and The Two Ronnies, died on Monday after a long period of heart trouble.
He died with his wife, Joy, by his side. Together they had three children, Adam, Larry and actress Charlotte Barker.
Adam Barker, from Ealing, was arrested on 3 June 2003 for allegedly having 1,200 indecent images of children on his home computer.
He was arrested as part of Operation Ore - the UK's largest ever police hunt against internet paedophiles.
He failed to meet police bail on 24 June 2004 and a Scotland Yard spokesman said at the time that he may have gone overseas.
On Wednesday, a Metropolitan Police spokeswoman said: "The Metropolitan Police Service is committed to safeguarding children through full and proper investigation of crime and assessment of risk.
"This is a particularly difficult time for the family and our deepest sympathy goes out to them.
"We will deal with the matter with the utmost sensitivity and will work with the family and their solicitors to achieve an appropriate and satisfactory conclusion."
Larry Barker told the Daily Mail his brother would not attend their father's funeral.
"Obviously Adam won't be there. There's no possibility of Adam being there," he told the paper. Ronnie Barker's agent declined to comment.