The presenter, who fronts the BBC ballroom show with Tess Daly, said she told bosses she was quitting when she thought filming clashed with 18-year-old Jake’s first day at uni.
Appearing on BBC Woman’s Hour, Claudia said dropping a child off for fresher’s week is “something parents have to go through” and recalled there being “plenty of tears” when she phoned Strictly’s executive producer to inform them of her decision.
Claudia said: ”’I phoned the boss of Strictly quite dramatically and said, through tears, ’Sarah I love you. I don’t want to leave Strictly and Tess and I have agreed we will leave together when they’re done with us, but if the first show is September 13, I’m out and you’ll have to go with somebody else.
“And there was a beat. And she said, ‘Quite dramatic. We don’t start that week.’
“I was like, ‘alright’. I have to go and put up his posters. It’s not that I love him more than others love their kids, but this is something parents have to go through.”
Claudia – who is parent to son Jake, Matilda, 15, and 10-year-old Arthur with husband Kris Thykier – had a pact with co-host Tess that if ever one of them were to leave Strictly, they would go together.
“Tess and I will leave at the same time,” she told The Mirror in 2019. “We’ve made that pact over pizza. We’ll go together, whenever they’re done with us.”
Claudia began hosting the Strictly results show in 2010 when the late Bruce Forsyth reduced his workload.
She stepped up to be his full-time replacement alongside Tess in 2014.
Strictly Come Dancing returns to BBC One later this year. Radio 4′s Woman’s Hour airs at 10am Monday to Friday and 4pm on Saturdays.