The farthing is a much older coin than the 1860s. The farthing as a unique coin dates from the start of the 13th Century, with the earliest known extent specimens from the reign of Henry III, but the actual practice is far older than that and dates back at least to the pennies of tenth century England. "Long Cross" pennies, such as this example from the reign of Æthelstan II, were specifically designed with the lines of the cross as guidelines for people to accurately divide whole pennies into halfpennies or foerđings. Given that the numismatic record gives us plenty of examples of earlier coins split into less precise halves and quarters, the emergence of the Long Cross type was presumably a tacit de jure acceptance of a long-running de facto practice.

Accurate pricing of goods beyond very specific examples from the Early Medieval period is quite tricky, however once we get into the High and Late Medieval periods, we have more extant textual evidence as to the cost of things. By the 1330s, for example, ale cost around .75d a gallon in Somerset or 1.5d a gallon in London, so a farthing would be a means of buying about 2 pints of ale, or about half a pint of best quality beer. It would also buy you about half a dozen eggs, half a pound of cheese, 2 herring, about 8oz (250g) of oats or roughly 4oz (about 115g) of dried fruit (depending on the fruit).

These are just a few values, but as you can see, it was a useful denomination for everyday Medieval use.

All prices are approximate, mostly taken from Myers' London in the Age of Chaucer and Dyer's Standards of Living in the Later Middle Ages.

E: FWIW, there were 12d in 1s, 20Ss in £1.

Have you not somewhat answered your own question? Several things on that list cost fractions of a penny, so there needed to be a coin that could represent a half-penny or a quarter-penny.

Similarly, looking at the specific list of prices you cite, the farthing is a much larger denomination than the modern penny is. While comparing historical prices to modern prices is fiddly because economies are complex and the relative values of things change, we can see how comparatively valuable a farthing was relative to the modern penny by looking at some examples.

Your list cites "ten loaves of bread" as costing 2s, 3.5d, or 27.5d or 110 farthings. That puts the price of one loaf of bread as 11 farthings, meaning "a farthing" could be thought of as "a sum of money equivalent to one eleventh of the price of a loaf of bread".

Looking at Tesco online, the cheapest loaf of bread in a modern supermarket (and this isn't an academically rigorous comparison) seems to be around 39p, meaning a modern penny can be thought of as "a sum of money equivalent to one fortieth of the price of a loaf of bread".

Obviously there are loads of things wrong with that comparison, the relative value of bread compared to other products may well be less now than it was a hundred and thirty something years ago, but the principle remains. All of the items on your list are relatively high-value (weeks' worth of groceries, relatively expensive one-time purchases) but still have average prices of which "a farthing" is a much higher fraction than "a penny" would be for equivalent purchases today.