She was in tears as she reflected on life with him in ITV documentary Derek's Story, which aired last night.
He died on January 3 after battling long-term effects of Covid-19 for over three years, damaging his organs.
The documentary showed his empty bed at home when he was in hospital in December after a cardiac arrest.
Later, Kate was seen in the same room, but Derek's bed was missing, replaced by a table and chairs - "a very different room now", she said.
Speaking on camera in February, Kate said: "This is the book he was reading, very slowly, at the end.
"I said to him, trust you to be reading A Little Life, because if anybody had a big life, it was Derek and it's left a big hole."
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