Wow your wife's a nurse, amazing! My wife's a GP so pull the other one.
They're still bound by a Government contract, they're paid by the government, their targets are set by the government, and the vast majority see only NHS patients and commission services directly from the NHS. They've moved the day to day management of the practice out of the Governements control, buts that it.
Very little has changed in the latest round of primary care restructuring really. The practices have always got a pot of money with which they provided healthcare and ran their business. The difference is now they have more control over commisioning and day to day working, so if they get a cheap deal on corn removal from Bupa they can send their patients there.
It's nothing like how a private GP works in the slightest.