The British comedian, who struck up a friendship with Mirren after co-starring in two movies, Arthur and The Tempest, said that he has never met anyone with a better work ethic.
He told Parade magazine: 'She could get along with anybody but, yeah, I think we connected with humour.
'She has a beautiful work ethic and doesn't make a fuss about anything. I've never met anyone more worthy of the title Dame.'
Brand, who married singer Katy Perry in October, added that although he has achieved Hollywood success, he won’t be turning his back on his comedy roots.
Asked if his stand-up days were over, he said: 'No. I love stand-up more than anything. If you're talking, why not make people laugh?'