I have used my work supplied private health insurance for the first time recently and didn't enjoy the experience at all. Although i couldn't fault the consultant, care, facilities etc, the nagging thought throughout it all was, "am i covered for this" "that treatment sounds great, but am i covered" The experience of having to phone up to seek "permission" to get treated was not something that i would want to have to do as routine.
NHS is not perfect, but i have never worried about the cost or payment, only getting better.
Sure but you still have the NHS option there as a back up. It's is hardly much of a worry re: private cover.
You generally are covered though if your gp refers you to a specialist then generally you go see that specialist. If you're with one of the big insurers your consultant already likely knows what is covered. In fact you can make sure you see a consultant that charges within the guidelines of the insurer - just phone them and ask. If you do find one that doesn't then it generally isn't a big deal, the procedures/tests are pretty standard at any private hospitals that work with the big insurance companies(else they'd not have many customers!) and you'd just need to cover the extra fees for the consultation... like maybe you get someone who charges 230 and your insurer only covers 200 say.. well it hardly breaks the bank to pay an extra 30.