Both William and Kate sported pins showcasing the yellow and blue colours of the Ukrainian flag.
They heard about the services offered at the centre and the huge number of donations they had received following Russia's invasion of the country.
William told volunteers that the UK and Europe were united on their side and spoke of his shock at seeing the war unfold.
"It's very alien to see this in Europe. We are all behind you," he said, adding that he, like many, wanted to do more to help. "We feel so useless."
The Cambridges offered assistance from their charity for young people and children suffering trauma and mental health problems due to the conflict, revealing their eldest children George, 8, and Charlotte, 6, had been asking questions about the tragedy.
"Ours have been coming home asking all about it," William said. "They are obviously talking about it with their friends at school."
He admitted it was difficult to discuss it with them, saying he had to "choose my words carefully to explain what is going on".
William and Kate took part in sorting and packaging donated items and spoke with the CEO of the Disasters Emergency Committee Saleh Saeed to learn more about the ongoing conflict.