With the Queen leading the way, the pair toured the Bush House facilities and met supporters of the development, as well as visiting a roof terrace that boasts panoramic views of the capital.
At one point, Kate could be heard describing the cityscape as “impressive”.
They then went on to view a robotics demonstration, including robotic surgery, and a demo showing how sensors made from textiles can measure useful information about the body.
Shaking a robotic hand, a beaming Kate joked: “Very nice to meet you.”
Wearing a grey Catherine Walker coat for the engagement, Kate looked elegant in the perfect winter attire as she waved to fans outside.
Meanwhile, Her Majesty also looked impeccable in a Stewart Parvin old rose cashmere coat with a silk dress of autumnal woodland in shades of grey, fuchsia and olive, teamed with a matching Rachel Trevor-Morgan hat.
Earlier in the week, the Queen joined the Duke and Duchess of Sussex for the christening of Zara and Mike Tindall's youngest daughter Lena.
Held at St Nicholas Church in Cherington, Gloucestershire, it was a low-key family affair.