Tony Blair said the celebrations of Baroness Thatcher's death were in "poor taste".
Speaking to BBC Radio Ulster, he said: "Even if you disagree with someone very strongly, you can still particularly at the moment of their passing, you should show some respect."
Mr Blair was asked if he worried there would be similar celebrations when he dies.
He replied: "When you decide, you divide. I think she would be pretty philosophical about it and I hope I will be too."
Read: Margaret Thatcher's legacy.
Read: Thatcher funeral next Weds.
This amateur footage of people celebrating Baroness Thatcher's death in Brixton has been uploaded to YouTube
In Brixton, demonstrators have gathered to 'celebrate' Baroness Thatcher's death and the lettering of the Ritzy Cinema has been rearranged to say "Margret Thatchers dead".
The south London district was the scene of fierce rioting during the Thatcher years blamed on deep social divisions, racial tensions and unemployment.
In the aftermath of the 1981 Brixton riots, the prime minister was criticised for what some saw as a lack of understanding or denial of the causes of the disturbance, after comments such as:
"Nothing, but nothing, justifies what happened.
"Money cannot buy either trust or racial harmony."
The prison officers' union says a gang culture inside an immigration centre in Lincolnshire is putting lives at risk.
Five officers at Morton Hall were injured during riots over the Christmas period. The union's now called on the government to take urgent action. David Hirst reports.
Five prison officers have been injured during a disturbance at an immigration detention centre. It's the latest in a series of incidents at Morton Hall in Lincolnshire. David Hirst reports.
Illegal immigrants have injured five officers during a riot at a detention centre in Lincolnshire, according to border officials.
Up to 40 detainees were involved in the incident at Morton Hall immigration removal centre in Swinderby, Lincolnshire, which saw one detainee taken to hospital and led to 12 others being transferred to other centres.
Staff were injured on December 30, the UK Border Agency said, while up to 50 detainees were also involved in a protest on Christmas Day, in which no-one was injured.
Both incidents, at the former women's prison. were brought under control within an hour.
Morton Hall was opened as an immigration removal centre in 2011. It holds up to 392 foreign national offenders, failed asylum seekers and illegal immigrants.
In September last year, 18 asylum seekers went on hunger strike at Morton Hall because they did not want to be sent back to Afghanistan.