The 25-year-old barrister was targeted as she walked her dog with her boyfriend and some friends. Two men demanded money and jewellery, but fled empty handed.
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The attack, which left Kathryn stunned but unhurt, happened shortly after 8pm on Monday evening on a Marylebone street not far from the £975,000 home her father bought her in 2010.
It was thought to be the second that the perpetrators committed that night.
"We were alerted at around 8.30pm to two robberies in the street in the Marylebone area," a Scotland Yard spokesman said. "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."
The news has also been confirmed by the Blair family, who said in a statement, "Kathryn was with a group of friends. No one was hurt and nothing was stolen."
A neighbour of Kathryn's told the Mail, "She must have been absolutely terrified. I can't imagine what must have gone through her mind when she saw a man pull out a gun. My first thought would have been terrorist.
"She's a lovely girl and we are just relieved she is ok. Part of her charm is that she is so down to earth. You would hardly believe her connections unless you knew her as she appears to live such a normal life. But this highlights the danger of not living amid all that security."
The failed robbery came just two days after Kathryn was pictured attending the wedding of her older brother Euan, 29, and his long-term girlfriend Suzanne Ashman, 25, in Wotton Underwood, Bucks.