Yes, the US has a fine organization known as the Veterans' Administration. It's a pity we haven't introduced it into the UK. Here our wounded servicemen get taken around the back of NHS hospitals so as not to "upset" or offend the civilians. And don't even ask about how ex- military people get treated in the UK. We used to have a handful of military hospitals, but I believe that they're all gone now.
Now you really haven't seen Sicko have you, pity that the 9/11 rescue workers don't get the same treatment and no surprise that Cuba gave them free treatment. Nice publicity stunt for Castro!
These are not my ("silly") ideas, but those that I have heard about. Such as these are under consideration by those charged with providing a service of ever-increasing (ever-demanding) proportions.
Ah yes I'm wondering if perhaps the first people to come up with that idea didn't have a
final solution 
The problem with that idea would be that those born mentally handicapped and children with leukemia would be penalised for either being born or just being sick. As for pensions your scheme would turn the pension system into a lottery for those who are lucky to have not had a day sick in their lives.
In your finally paragraph you've also brought a separate issue into play that of health holidays. My idea would be to make it a legal requirement for visitors to the UK to have medical insurance. Also limit the issue of visa's on arrival in the UK to a small number of countries (ie EU/USA) and require the rest to get a visa at a British embassy. Then if anybody arrives in the UK without the necessary documents fine the airline that permitted them to fly just like truck drivers get fined if stowaways are found in their trucks.
I'd also send representatives of the UK customs and immigration service to Australia, if we had their border control it would certainly improve things.
As for the NHS, as I mentioned a lot of changes seem to have been made more for politicians political agendas than to help the NHS. So I'd grant the NHS more independence from government so it can get on with it's job without having to play politics.