Reading about coffee production in the UK during this period, one finds references to coffee being adulterated with all manner of substances, some more unfortunate than others. A law of 1718 refers to "divers evil disposed persons who... made use of water, grease, butter, or such unwholesome materials" in the making of coffee, and in 1803 the use of burnt or scorched peas and beans for imitation coffee was prohibited. Investigators in later periods found additives ranging from acorns to powdered horse liver being included in coffee. During one such investigation, the beverage sampled was described as "the most infamous stuff, hot to the mouth and unfit for human food." (Which does beg the question as to what temperature coffee was commonly served at.) However, one would hope that these English coffee merchants were not using such additives in their home preparation.

It's possible that the coffee beans they were trading in may have been lower quality than other varieties. One pamphlet writer in 1774 described coffee from West Indies plantations as having "something in the smell, a rankness in the taste, and disgusting return, especially of that from the English islands." Apparently growers in the British dominions (primarily located on Jamaica, but also Grenada and other islands) preferred to grow coffee in moister lowland soils, which could produce yields five to seven times higher than in better drained upland plots, but at a cost to quality. In addition, coffee berries should ideally be picked at a certain stage of ripeness, but the Caribbean plantations were worked by enslaved people under the threat of harsh punishment if they failed to meet their picking quotas, so were understandably not as concerned with correct ripeness as a free farmer in Yemen or the East Indies. In general, it seems the focus in all stages was on bulk production rather than quality, from siting the plantations to picking to processing of the beans.

In terms of how the English prepared their coffee at home, a book of 1722 instructs people to roast their beans in a metal vessel full of holes over an open fire, then to grind the beans and store for up to three weeks in a sealed bottle. When brewing, apparently coffeehouses would typically add coffee grounds to a boiling pot of water on the fire, while this author thinks it best to add the grounds to a kettle, pour hot water over them, and let steep for five minutes. That sounds fairly reasonably to my modern ears; not exactly a "villainous mode" of preparation as mentioned in the question.

However, this was early in the century, and practices may have changed by the time Kant was an adult. I find several references to the French developing new techniques for infusion during the 1700s, such as placing the coffee in a linen or flannel bag to keep the grounds out of the finished drink- perhaps the English merchants were still preparing their coffee Turkish style, with the grounds left in the cup, and this was considered outdated by people on the continent? I'm not sure I can say, based on the sources I have available. Hopefully a food historian can come by to say more!

In any case, I'll leave you with this aside from the coffee-brewing guide I found. The author tells of a man who had terrible rheumatism in his shoulder, to the point that he could not lift his hand to his head. His condition resisted all treatment, despite "continual Use of Opiates," but one day he was cured entirely after "Drinking a full Quart of Strong Coffee." And if that's not an endorsement of English coffee brewing, I'm not sure what is.

Main sources used:

Accounting for Taste: British Coffee Consumption in Historical Perspective, by S.D. Smith

Poor Consumers as Global Consumers: The Diffusion of Tea and Coffee Drinking in the Eighteenth Century by Anne E. C. McCants

The Domestick Coffee-Man, Shewing the True Way of Preparing and Making of Chocolate, Coffee and Tea, Etc by Humphery Broadbent