Barrister Kathryn Blair, 29, came face to face with the thieves as she and her boyfriend were walking their dog shortly after the wedding of her brother Euan.
The two men, one armed with a gun, demanded cash and jewellery before suddenly fleeing empty-handed.
The former Prime Minister’s daughter and her partner were shocked but unhurt.
It is believed Ms Blair and her boyfriend were threatened near her townhouse in Marylebone, central London on Monday evening.
The pair had spent the weekend with father Tony and mother Cherie in Buckinghamshire for Euan's wedding to Suzanne Ashman.
One security expert told the Express: “It seems staggering that the daughter of man who evokes such extreme emotions in some should be wandering around in the dark at night without protection.
“To think she had a gun pulled on her and was effectively defenceless raises massive questions about her personal safety.
“Thankfully she came to no harm but the potential terrorism threat is obvious.’’
A Scotland Yard spokesman said: “We were alerted at around 8.30pm to two robberies in the street in the Marylebone
The first happened at 8pm and was carried out by a lone suspect. The second occurred approximately 30 minutes later.
“We believe both robberies were carried out by the same male suspect though on the second occasion he was accompanied
by another individual.
“Neither of the two victims were injured. A firearm was shown on each occasion though no shots were discharged.
“Officers are investigating both robberies. There have been no arrests at this stage.
“We believe nothing was stolen in one of the robberies. We are still investigating the details of the other."