I think it is rare for insurance to cover (unless your work gives ygives you a swanky is-style package) but worth checking! Mine is covered as I have to have a csection due to previous csections. I was amazed when they told me I would be covered if I had another child when I called up a few years ago to add my last child to the policy! It would have never crossed my mind!
Excesses and consultant fees still add up even with insurance and late switch over though- I'm not expecting much change from about £6k.
That said, it seems to be the delivery fees for the hospital that are the biggest chunk at about £10k all in for a csection. Very nice to be covered for that as wouldn't have been an option orherwise