Daly has hosted the BBC One show, now in its 20th season, since it began - originally with Sir Bruce from 2004 to 2014, and now alongside Claudia Winkleman.
She admitted that her first day in the job had been terrifying, particularly being matched as co-host with the veteran broadcaster, but said that he soon put her at her ease by putting the kettle on.
Daly said: "I remember being so intimidated because I was working with the late, great, Sir Bruce Forsyth, someone who I had grown up watching on the television with my family, and it was pure pinch yourself stuff.
"He was such a gentleman and made me feel immediately at ease by offering to make me a cup of tea. He popped the kettle on and made me the perfect cuppa, and I just remember thinking, ‘oh my goodness, he's just like the rest of us.’
"He was just so down to earth and so generous with his time and himself, so from that moment on I just began to enjoy the ride."
Sir Bruce retired from the main show in 2014 and died in 2017, aged 89.
After he left Strictly, Winkleman took over as co-host with Daly, having previously presented spin-off show It Takes Two.
She told how some of her early series on It Takes Two had been very different in real life to the glamorous image viewers saw - including battling morning sickness on air during the live show.
Winkleman said: "On It Takes Two I had morning sickness and there was this a bucket behind the chair as I would throw up during every VT, which was really quite a lot for the crew to deal with.
"When my son was one I would take him to work and he would often be hiding behind a sofa with a toy."
Watch: Who is Strictly's Hamza Yassin?