Yep, you're essentially paying for the administration costs by going private, but that's not what the Bupa adverts sell you, and it's not what people seem to assume when you say you've got private healthcare. They think you're in some kind of special institution where you're pampered 24/7 by medical professionals, when in reality you're in the same NHS bed as the person next to you with some minor benefits. Additionally, as you've rightly pointed out, your private insurance will only cover non-existing illnesses. A&E isn't covered, nor is anything that might've existed before you picked up your insurance, and they'll be sure to check up on that. Take away the NHS, and the infrastructure becomes fully private, and that's when the costs will go through the roof.

For the life of me, I don't know why this isn't what Labour are driving home to people. They should be telling people "Vote Labour, or kiss the NHS goodbye".