This is rather a tricky one.
My feeling is that a nanny with a rubbish car, would be quite happy... whereas other nannies with good cars, would not.
Insurance could be a headache, as more and more policies do not allow you to drive someone else's car, so you would need to become a named driver, and nanny be named on your policy.
Not fully sure on the company car rules, but you would need to look into that, as you would be providing your employee with a car.
As you have isofix car seats, switching them between cars is not going to work in the majority of cases. My car is 3 years old, it does not have isofix. I don't know how old many nannies cars are, but I would expect that isofix is not common enough yet for a typical nanny to have it in their car, especially for two isofix seats.
The car itself isn't the only issue, there is also the drivers ability to drive the car. Some nannies are quite young and thus may have only a few years driving experience. In nannying as a whole, experience counts for a lot... driving children around in a car is the same, a inexperienced driver who has never driven children around in their car, could be far more easily distracted.
Tricky one. Depending on what you decide to do, it could severely limit the number of potential nanny applicants.