Yes, it’s crucial. The car’s insurance must cover the supervising driver.
If you are driving your own vehicle, you must have learner driver insurance with the supervisor as a named driver on your policy.
However, if you are driving someone else’s car, such as Mum or Dad, you’ll either need to be named on their insurance or take out “Named driver insurance.” This allows you to drive a car belonging to another person without affecting their no-claims bonus.