I must confess that you Brits "were" on the cutting edge when it came to taking care of the poor. The first poor law was passed in the 1500's and by the 17th Century, almost a fifth of the English population had received alms at one time or another.
However, it should be noted that the poor laws weren't passed so much out of compassion as to keep the beggars off the streets who were stealing and terrorizing the country.
So it would be a good guess to think your healthcare system was probably borne out of the same mind-set.
You are certainly correct about the heathcare not being free in Britain. My husband has WAY more money taken from his paycheck for the good old NHS than our private insurance in the states costs and our private insurance is excellent.