Private healthcare is not the answer- firstly, it isn't available to all like the NHS (small details etc permitting) - I understand your frustrations at the wait and hope there is a cancellation for you soon. Bear in mind that private patients get treated by NHS doctors that also do private work. When I worked in the NHS these doctors favoured and spent more time on those patients that paid. Private patients also often use the same resources that NHS places do ie scanners, staff, doctors etc etc, so it doesn't address the problem - allows for greed in some doctors that are already paid huge salaries and continues to create an elitist moneyed system. The NHS needs more input and don't get me started on the cost of certain services and medicines etc.
I would like to correct you on that one.
The NHS is moving towards "Any Willing/Qualified Provider" for commissioning healthcare. Your local Primary Care Trust could, in theory, refer you to a private provider if the cost is comparable to the NHS.
I work for a private Healthcare provider and we have a patient from "up north" travelling over 200 miles who is booked in for an NHS paid-for pain management procedure next week.