Bin Laden, blamed by the US for the 9/11 attacks, was killed by US forces about 62 miles from Pakistan's capital.
Prime Minister David Cameron hailed the death as "a great success" but said it was not the end of terror threats.
Foreign Secretary William Hague said the network may try to reassert itself.
Mr Cameron said early on Monday, just hours after US President Barak Obama confirmed the death: "The news Osama Bin Laden is dead will bring great relief to people across the world."
He later spoke from the prime minister's country residence, Chequers: "This news will be welcomed right across our country. Of course, it does not mark the end of the threat we face from extremist terror - indeed we will have to be particularly vigilant in the weeks ahead. But it is, I believe, a massive step forward."
Following Bin Laden's death, the US put its embassies around the world on alert, warning Americans of the possibility of al-Qaeda reprisal attacks for Bin Laden's killing.
Mr Hague also stressed the likelihood of reprisals against UK targets.
"We must remember that this is not the end of being vigilant against al-Qaeda and associated groups, and, in fact, there may be parts of al-Qaeda that will try to show that they are still in business in the coming weeks, as indeed some of them are.David Cameron: "It is a massive step forward"
"So I have already this morning asked our embassies to review their security, to make sure that vigilance is heightened - and I think that will have to be our posture for some time to come.
"This is a very serious blow to al-Qaeda, but like any organisation that has suffered a serious blow, they will want to show in some way that they are still able to operate."
Bin Laden was top of the US "most wanted" list, and President Obama said his death was "the most significant achievement to date in our nation's effort to defeat al-Qaeda".
In the attacks in New York and Washington on 11 September, 2001, 67 Britons were among the 3,000 people killed when four planes were hijacked and flown into New York's World Trade Center, the Pentagon and a field in Pennsylvania.
Tony Blair, UK prime minister at the time of the attacks, expressed his "heartfelt gratitude to President Obama and to all of those who so brilliantly undertook and executed this operation".Continue reading the main story
Frankly there were periods during those 10 years when it was far from certain where Bin Laden was or even that the trail had not gone cold”End Quote Douglas Alexander Shadow Foreign Secretary "We should never forget 9/11 was also the worst ever terrorist attack against UK civilians, and our thoughts are with all those - American, British and from nations across the world - who lost their lives and with their loved ones who remain and who live with their loss.
"The operation shows those who commit acts of terror against the innocent will be brought to justice, however long it takes."
Mr Cameron said it was "a time to remember all those murdered" by Bin Laden, and he congratulated Mr Obama and others responsible for carrying out the operation.
"Osama Bin Laden was responsible for the worst terrorist atrocities the world has seen - for 9/11 and for so many attacks, which have cost thousands of lives, many of them British," Mr Cameron said.
"It is a great success that he has been found and will no longer be able to pursue his campaign of global terror."
Bin Laden evaded the forces of the US and its allies for almost a decade, despite a $25m (£15m) bounty on his head.
He was killed in a firefight in a fortified residence in Abbottabad, 100km (62 miles) north-east of Islamabad.William Hague: "We should be relieved that Osama Bin Laden's terror... is now at an end"
The property had 4m-6m (12ft-18ft) walls, was eight times larger than other homes in the area and was valued at "several million dollars", though it had no telephone or internet connection.
Mr Hague acknowledged that there had been a "general assumption" that Bin Laden was hiding in the mountainous, tribal regions of Pakistan rather than the area around the capital, Islamabad.
But he added: "I don't think we're surprised by anything any more."'Huge setback'
Shadow foreign secretary Douglas Alexander said he agreed with Mr Cameron in congratulating the US special forces.
He too emphasised the need to remain vigilant, but added: "It is a huge setback for al-Qaeda, because the survival of Osama Bin Laden had become part of the propaganda that they were using to try and bring people to their hate-filled ideology."
Mr Alexander said there had been a continued international focus to bring Bin Laden to justice, "but frankly there were periods during those 10 years when it was far from certain where Bin Laden was or even that the trail had not gone cold".
"There will be plenty of time for questions to be asked and answers offered," he said, adding that immediate steps needed to be taken to keep everybody safe.
He also said there needed to continued efforts to ensure that people in Pakistan and across the region understand that their best interests are served by following the rule of law.
Former Foreign Secretary David Miliband tweeted his reaction to the death of Osama Bin Laden, saying: "A day to remember the victims of terrorism and the bravery of our troops. But also a historic chance to build for the future."
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