If you have a condition now you will be seen the same day even if it's not an emergency. I had a high fever for a couple of weeks and finally decided to see a GP - got an appointment in 2 hours of the call to the surgery, GP told me to go to the ambulatory care department at the nearest hospital(nothing to do with emergency care there) and I was admitted and seen pretty much within an hour of arriving. Spent several days over the next month in and out of the hospital, had some treatments done = no bill was ever produced.

Also when my wife had to get an MRI done going private wasn't that much quicker than NHS - you still had to wait a couple weeks through her private health insurance at work.