Jordan, 29, and his brother Cian, 24, have since discovered they have a rare inherited gene that means they will develop dementia symptoms in their 40s.
Brian praised the brothers, who are raising awareness and funds for the charity to help find a cure.
Brian said: "I am full of admiration for Jordan. Not many people of his age would have the courage to accept their diagnosis the way he has."
Cox shared his own experiences from when his older brother succumbed to the illness. The actor revealed in an emotional film for Alzheimer's UK he had to reassure his brother Charlie he no longer had to go to school.
Brian said: "I had it in my family but at a much more advanced age.
"My brother was very funny, even in his dementia, because he would sit there and he would say, 'Hey, Brian, am I still at school?' when he was 70 and I'd say, 'No, Charlie, you're not'.
"He'd say, 'I thought so. I always remember the way he said, 'I thought so', as if there was a thing going on where actually there was a relief to him to know he wasn't at school any more. It was quite strong, very extraordinary the effect it had on him because it kind of relieved him."
The Dundee-born star added: "I will go on until I drop.
"You s...