The Queen said King Abdullah of Saudi Arabia "will be long remembered by all who work for peace and understanding" as world leaders marked his death amid renewed protests about the human rights record of his regime.
Prime Minister David Cameron and the Prince of Wales are to fly to Saudi Arabia tomorrow to join international figures paying respect in person to the royal family and flags have been lowered on key public buildings in London.
But the decision to fly them at half mast has drawn sharp criticism from some prominent politicians over abuses of free speech, women's rights and the country's role as cradle of Islamist extremism.
Abdullah, thought to be aged about 90, died yesterday after two decades in power in the world's biggest oil exporter. He has been succeeded by his 79-year-old half-brother, Salman.
In a statement to Salman, the Queen - now the world's oldest monarch - said she was "saddened" to learn of the death.
She said: "Your distinguished brother Abdullah had devoted his life to the service of the kingdom and the service of Islam.
"He will be long remembered by all who work for peace and understanding between nations and between faiths.
"I offer Your Majesty my sincere condolences and I offer my sympathy to the Saudi people."
Mr Cameron said that he was "deeply saddened" and that the ruler would be "remembered for his long years of service to the kingdom, for his commitment to peace and for strengthening understanding between faiths".
Former premier Tony Blair said he was a "stable and sound ally ... a patient and skilful moderniser" in a turbulent time in the region.
But the flags issue drew stinging criticism in the wake of Saudi Arabia's recent public beheading of a woman and a sentence of 1,000 lashes meted out to the creator of an online blog.
The leader of the Scottish Conservatives Ruth Davidson condemned the move as "a steaming pile of nonsense" and Ukip MP Douglas Carswell said it showed Whitehall officials held "immoral" values far from those of the British public.
Downing Street and other Whitehall departments - with Westminster Abbey and Buckingham Palace - were among prominent landmarks to put Union Flags at half mast after a request was sent out by the Department for Culture, Media and Sport (DCMS).
DCMS issued a notice that "all flags be half-masted from 8am today until 8pm this evening" although it said it was for devolved governments and individual town halls to decide whether to do so.
In a split between two of Ukip's key figures, leader Nigel Farage said it showed "respect for an ally in the war against terror" and that the issue of human rights should be taken up "with the new, not the old king".
But MP Douglas Carswell said officials had seriously blundered and showed "immoral" values far from those of the British public.
The decision drew criticism from many on social media - some of which was reposted by Mr Carswell.
"On the day that Sir Humphrey lowers the Union Jack in Whitehall to mark the passing of the Saudi monarch I wonder how many public executions there are going to be in Saudi Arabia?," he said - a reference to the name of a senior civil servant in Whitehall satire Yes Minister.
"Why are we doing this? I think Sir Humphrey has seriously blundered.
"Sir Humphrey's values need to be aligned more closely to people in this country rather than being quite so immoral. Saudi Arabia is a country that doesn't let women drive and publicly executes people."
But asked if Mr Farage was comfortable with the decision, a spokesman said: "Lowering a flag is an issue of diplomatic protocol, respect for an ally in the war on terror.
"We should forcefully take up the issue of human rights with the new not the dead king."
When Abdullah ascended the Saudi throne in 2005, he had already been the country's de facto ruler for a decade after his predecessor and half-brother, King Fahd, was incapacitated by a stroke.
In the terms of the ultra-conservative Islamic kingdom, he was seen as a reformer, chipping away at some of the severe restrictions on women - allowing them seats on the country's top advisory council and to attend mixed sex classes at the university he founded.
However there was a limit to how far he was willing - or able - to go, and Saudi Arabia remains the only country in the world where women are not allowed to drive.
More recently, the sentencing of the blogger Raif Badawi to 1,000 lashes threw a spotlight on the kingdom's harsh laws cracking down on any dissent against the ruling family.
Western governments - including Britain - have in turn been accused of turning a blind eye to such excesses in return for lucrative arms sales and the continuing flow of Saudi oil.
Following the 9/11 attacks on the United States in 2001, the kingdom was criticised as the cradle of a radical branch of Islam which gave birth to the extremism of al Qaida.
Abdullah eventually cracked down hard after al Qaida militants mounted a series of terrorist attacks aimed at toppling the monarchy.
In recent months however the Saudi authorities have been forced to deny they funded and exported an intolerant brand of Sunni Islam which gave rise to the brutal Islamic State insurgency in Syria and Iraq.
DCMS initially suggested that the formal request for flags to be lowered to half mast came from Buckingham Palace but later clarified that it was the role of the Department to issue it.
A spokeswoman said: "In line with long-standing arrangements, the Union Flag is flown at half-mast on Government Buildings following the death of a foreign monarch."
Westminster Abbey said not lowering its flag would have been a "noticeably aggressive comment" and would not have helped support the "desperately oppressed Christian communities of the Middle East".
An Abbey spokesman said: " We always fly a flag. It is at half-mast because the Government has decided to fly their flags at half-mast today.
"For us not to fly at half-mast would be to make a noticeably aggressive comment on the death of the king of a country to which the UK is allied in the fight against Islamic terrorism. Nor would it have done anything to support the desperately oppressed Christian communities of the Middle East for whom we pray constantly and publicly.'
Former prime minister Sir John Major said: "King Abdullah will be remembered as a peacemaker and reformer, whose moderate views sought both to stabilise the Middle East, and soften the most conservative opinion in Saudi Arabia.
"He was a good friend of Britain and a wise man whose voice will be missed far beyond his own country."