It may not need to be an either-or. As @Libaz points out, for the money the NHS is decent value. If you could bring in some charges maybe similar to how it is in France, you could build on what we have. Wouldn't want to throw the baby with the bathwater. The whole GP setup needs some revisions. Charging £5 to £30 an appointment (unless on benefits) might help, and stop people taking the tinkle, plus improve the level of care. At the moment, you're not a customer, GPs are overworked and forced to act more like civil servants than healthcare workers.
Gps choose how many patients they take. They choose how long they see a patient. They are not a part of the nhs. They are small businesses that charge the nhs.