The Duchess praises the efforts of staff, some of whom were also on duty on the night of the Westminster attack in March.
A total of 14 people suffering predominantly with stab wounds were admitted to King's College Hospital shortly after the attack.
Many of the staff at King's College who tended to the trio's victims had also been on duty on 22 March when Khalid Masood killed five people in an attack on Westminster Bridge.
Kate said: "To go through this sort of event twice, it is quite unprecedented."
Talking to the Duchess about the "trauma" of the incident, the hospital's head of nursing Lynne Watkins-Hulme explained: "We are used to seeing people who are stabbed.
"But to have six women who were stabbed, multiple times - it was just the amount of people - that was upsetting."
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Emergency consultant Malcolm Tunnicliff, who rushed to the hospital on hearing of the atrocity, said staff used a week's worth of kit in just an hour and a half.
When asked what he took from Kate's visit he said: "It gives the patients a lift, it gives the staff a lift that they're being recognised.
"And actually, all staff in the NHS want these days is just to be recognised for what they do, because they get knocked for so much.
"Someone like that coming along and recognising that, it is a massive lift."
Meanwhile, evidence of the attack can still be seen in Borough Market, with bullet holes clearly visible in the metal shuttering on the fruit and veg stall opposite the Wheatsheaf pub where the three attackers were killed.
As stalls and businesses attempt to return to normal, jet cleaners are being used to wash down the pavements ready for the market to open on Wednesday morning.
Traders will hold a minute's silence in tribute to victims at 9.30am, before the market bell is rung at 10.00am to mark the return of shoppers.