Kate also had to contend with her beloved car, nicknamed Vicky Volvo, being stolen from outside her London home.
But, she said, the reaction from supporters offering to help had been overwhelming in a "heartbreaking" time.
Her co host Ben Shephard explained: "The car was stolen which we are all furious and frustrated about.
"But that’s not what we want to talk about, the thing we want to talk about is the outpouring of support you have had from people, viewers, companies.
"Oh, unbelievably! So nice, so nice," said Kate, who said it was their first car as a family.
"And it's been kind of a tough old week for Derek, so I haven't got back to anybody and I haven't sorted it out yet.
"But it's been so lovely, and some viewers even offered to lend me their cars, which obviously you have not spoken to Ben Shephard!"
Ben, who had been teasing Kate for her driving skills, joked: "Don't do it!"
"Don't be mean!" she scolded him. "People are really moved."
"Honestly I am constantly blown away about how lovely you've been about all of this, and it's that kind of generosity and kindness that will get us through.
"After Piers [Morgan] mentioned my car was stolen last week, I was talking to the hospital and it happened to a nurse, she finished her shift, where Derek is, came back and her car was stolen.
"She must have just been at the end of her tether with exhaustion, and weirdly enough I now realise there is a real premium on second hand cars at the moment.
"There are on a real premium and people are stealing them. I know times are tough and people are turning to things they shouldn't, but honestly, it is just heartbreaking.
"It's an intrusion, it's yours, and in the case of a nurse, it's people at the end of their tether."
* Good Morning Britain airs weekdays on ITV at 6am