your thing about GPs isn't quite correct. GPs are on the NHS payroll - they can't make profits - they don't buy their assets (the NHS does) - but they do run a little business on behalf of the NHS.
Its supposed to create an internal market but not sure it quite works.
I'm the OP AC. Your point is basically wrong. GP practices are private, for profit businesses.
Originally pre NHS doctors were essentially sole traders and did house visits because that was what people would pay for when they were sick. They became partnerships because after the NHS was formed it was discovered that a better business model was to group together, buy a building, hire a receptionist etc and then get the sick to come to you. Eliminating travel time increased the number of patients the doctor could see, and colocating two or three doctors in one house meant that they could split the costs of buying a house etc while sharing the profits. The later improvement on this in established businesses was bringing in GP's as saleried employees of a practice so they did the work but the partners of the partnership take the majority of the profits. (capitalism at it's finest, even in healthcare. ;) )
Some NHS trusts have employed a few saleried GP's directly and usually co-locate them with A&E, largely to meet the 24/7 care requirement introduced a few years ago as it was difficult to get GP practices to do it at any reasonable cost, and it saves the NHS trust money.
Say the billing rate for a GP to assess my cough is a cold and doesn't require antibiotics is 100%. If you goto your GP then they bill 100% to the NHS trust, which duly pays it. If the NHS trust runs it's own service next to A&E which you visit instead, and it only cost them 70% to provide then they bill themself 100%, and make 30% "profit" on the service they provided.
Hence why I say that the NHS is more of a brand and billing structure than an organisation. Look at how the NHS was formed and you'll start to understand it a bit.
Biting the hand that feeds IT
