In the middle of the eighteenth century, "health care" was delivered in a very different way than today. If you had the money, you hired the services of a medical man and got treated at home. There were very few hospitals, and only the very poor and very desperate would enter them. "Doctors" of many sorts abounded, as compulsory education and qualification for them only came in 100 years later. There were well educated physicians, who had attended university. There were surgeons, who had served an apprenticeship and sometimes travelled to London to get a bit more experience. There were apothecaries, who sold remedies. They all worked for a fee, and on the whole, if you had no money, you had no treatment ( not necessarily a bad thing, if you consider some of the treatments!).
At that time , Newcastle was becoming prosperous, mainly due to coal. The Mayor, Matthew Ridley, was enlightened, for the times, having given free fuel to the poor during the famine of 1739-40. Altruism towards the poor was growing, with the founding of hospitals for them in many great cities. At the instigation of a local doctor, the demand was made for an Infirmary for Newcastle, and popular opinion carried the idea into reality.

Ridley, Ingham and Blackett
From here, enter the Newcastle Infirmary time line
Dr G Enever, 25/05/01