Kathryn Blair, 25, a barrister, was targeted as she walked down a central London street with her boyfriend and a group of friends, the BBC reported.
Police confirmed an incident involving two male suspects with a gun took place in central London on Monday evening.
"The victims were a man and a woman; the suspects were two males," they said in a statement, adding the incident was being linked with another attempted robbery nearby 30 minutes earlier.
"On both occasions a firearm was seen but not used - no shots were fired. None of the victims were injured and nothing was stolen during the incidents," police said.
It said investigations were under way but no arrests had been made. A spokesman for Tony Blair's office could not be reached for comment.
Blair, 60, was in office from 1997-2007 and involved Britain in the deeply unpopular invasion of Iraq, something which ultimately helped end his political career. Based in London, he now presides over a network of global consultancy businesses and charities.
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@umer: In UK, a Prime Minister can lie and get 1,500,000 people killed in Iraq and roam all over the Western Civilization giving lectures on human rights.
In UK an ex PM's kid get held up on gun point. In our's ex PM kids get kidnapped and remain so for 3 odd months! What ever we do, we do it grand!