Bush, Blair and their wives posed grim-faced for reporters in front of the black front door of the prime minister's official residence, before stepping inside, followed by several members of Bush's large entourage.
Reporters shouted questions to the leaders, but neither replied.
At least 17 people were reported killed and more than 350 injured in two bomb attacks Thursday on British targets in Turkey's largest city, Istanbul, which the British government said had "all the hallmarks" of the international terror group al-Qaeda.
Foreign Secretary Jack Straw, who gave Britain's first reaction to the atrocity, said the explosions would be "a major subject of discussion" between the two leaders.
Bush, who is continuing a state visit to Britain, was to hold a press conference with Blair at 12:15 GMT.
The two men were also to hold a working lunch.
Bush was preparing to leave Buckingham Palace - where he is staying three nights as the guest of Queen Elizabeth II - to lay a wreath at a war memorial at Westminster Abbey when news of the Istanbul explosions came in.
During a four-minute ceremony, Bush presented a wreath that said simply "In Remembrance" at the black Belgian marble tomb of an unknown British soldier from World War I in memory of war dead who are "lost but not forgotten".
Bush was also to meet yesterday with a small number of the families of the more than 50 British soldiers killed since the March invasion of Iraq and subsequent US and British occupation.
A Ministry of Defence spokesperson declined to give details of the private meeting for security reasons.
He said: "He is meeting a representative sample of families – a cross-section of different services, ranks and causes of death.
It is a small number of families". – Sapa-AFP.
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