Michael D Higgins says the Eurovision songwriter's death "will have been heard with sadness by so many".
The star, who appeared on the seventh series of Big Brother in 2006, had been fighting anorexia.
The BBC had said there would be "special coverage" on its networks after the duke's death on Friday.
The permanent closure of a top venue symbolises the struggle many performers are facing.
Tahar Rahim has been nominated for his part in The Mauritanian.
What was it like to take on the part of the Duke of Edinburgh in the award-winning Netflix series?
What was it like to take on the part of the Duke of Edinburgh in the award-winning Netflix series?
The TV presenter discusses his new ITV game show and why he really, really hates autocue.
The TV presenter discusses his new ITV game show and why he really, really hates autocue.
The US performer, whose real name was Earl Simmons, suffered a heart attack earlier this month.