My wife needed her gall bladder removed. She had many gallstones that were causing her extreme pain, which needed many trips to A&E to get Morphine based pain killers to deal with. Mind you, she has a very high pain threshold. The NHS waiting time for the removal was 2-3 years.
Fortunately I have private family health insurance through work, so we went with that route. The time from referral, to having the operation was 4 weeks.
4 weeks of pain vs 2-3 years... it's easy to see why people prefer private.