There might be. The US government spends way more money per head on public healthcare than the UK (and only slightly less than Norway) and that's totally separate to all the private spending! http://www.theguardian.com/news/datablog/2012/jun/30/healthc...
Procedures are so expensive, doctors so highly paid, and insurers so profitable that the US is essentially subsidizing all that while still not providing universal healthcare.
In the UK we're both taxed less AND don't have to have private insurance due to the above. (It does have some downsides though, particularly in not being able to easily 'shop around' or get access to cutting edge/experimental medicine.. it's a bit one size fits all.)
A top-level policy with Bupa/Pru will get you easy access to top hospitals in the UK (including London), for diagnostics at least. I just got a quote for £70/mo (it will almost double if you claim, however).
EDIT: hm, not sure about 'experimental', but top quality/teaching hospitals anyway.
Nobody in the United States gets access to cutting edge/experimental medicine either. Insurances just won't pay for it. They say "too experimental" and "not medically nessessary" is a reason not to pay. I am currently in a 3rd level of appeal to get my insurance company to pay for my medication they claim is "too experimental" (it isn't by the way!!!)
