Look for Group 1 insurance. Small cars like VW UP/Skoda Citigo/Seat MII (all same car) or Aygo/Peugeot 108/C1 (all same car) can be had relatively cheaply if looking for a 5-8 year old car and insured as cheap as you’ll get.
Insurance is expensive. No getting away from it.
Ways to make it a bit cheaper include having DC as main driver and then adding a couple of experienced adults as named drivers.
If your DC doesn’t need to be a main driver (for example if they will go off to uni and leave car behind) then some families get a small run around as family 2nd car. They put a parent as main driver (as lomg as they actually are- otherwise illegal and Fronting) and have DC as named driver.
If your DC is main driver, they build up their own non-claims but won’t if only a named driver.
We made it a bit cheaper by trading in our old 2nd family car for one of the small ones listed above. This is DHs car. He drives it most sand is insured as main driver. DC is a named driver. They drive it less than DH and across the year, it will be substantially less as he goes to uni the autumn so then won’t drive for 10 weeks at a time. For us, we only need 1 bigger family car - myself and DH drive that and take it on holidays etc. the runaround can be driven by any of us plus DC. We did t need 3 cars in the family.
I think lots of families buy a 3rd car for a teen new driver/learner when they do t actually need 3 cars in the household - esp with more people home working etc. Sometimes it’s because 1 adult doesn’t like the idea of driving a smaller starter car like an Aygo etc. In most families with 3 drivers, there are only few times when all 3 will be out in car at once, so for many just having 2 is a big money saver.
My DC probably won’t own a car until he’s in work full time at maybe 22/23. He won’t build any non claims until then, but by then he will be able to say he’s been a named driver and (hopefully) accident free for 5 years and being a bit older will make it a bit cheaper.
It’s best approach for us anyway.