There were many other reasons as to why the "democracy" (even though the extremely corrupt, unstable and tyrannical French Republic governments could barely be called democratic in any genuine sense) as seen during the French Revolution was spurned by many people in Britain, rather than just the practicality of it. It was an overtly atheistic and anti-religious movement, which disgusted and horrified much of the still devoutly religious lower classes in Britain (just as it did in the French countryside). Even though the violence and persecution was directed against Catholics, who the British generally disliked, it was the larger principle that upset them. Additionally, the unethical mass imprisonments and executions of political enemies was viewed with horror; that type of arbitrary and aggressive rule was basically unheard of in modern Britain, and even seemed extreme compared to the ancien regime.

The British also had a more nuanced view of democracy and representative government than simply "no monarch = democracy". The deeply ingrained tradition of parliamentary co-existence with the monarch over centuries had created a relatively acceptable compromise of representative government (the House of Commons) and retaining the monarch. Both of these different sources of power were viewed as necessary counter-weights to each other, one stopping the other from gaining too much power and asserting total supremacy. They remembered the persecutions and unjust rule that occurred when the Parliamentary faction won the Civil War in the 1640s. Though the representative nature of the House of Commons was not without flaws, it was viewed as essentially the best thing the people could hope for, in the 18th century.

Thus, the British viewed the evils of the French republican governments as being caused by both their atheistic beliefs, as well as their total disregard of tradition. Religion and tradition were extremely important to the British in this era, and held as a badge of honour (one of the reasons why even today Britain does not have an explicit written constitution, rather a myriad of traditions encompassed in "common law"). The opposition to the French Revolution wasn't necessarily strictly because of its supposed democratic nature, but because it devolved into what was often described as "mob rule" (including by Napoleon himself). As mentioned earlier, the British held dearly their own form of representative government via the House of Commons (a system which proved far more long-lived than any of the republican French systems).

tl;dr: It was the combination of atheism/anti-religion, rejection of tradition, and the violence of mob rule that gave most of the British a negative impression of the French Revolution, not the basic tenants of representative government and fighting tyranny. Remember, a sizable part of the British public supported the American revolutionaries only a decade before, specifically because they viewed it as their right for parliamentary representation. Since the Americans did not, unlike the French, devolve into an orgy of persecution and executions, it was viewed favourably.

Edit: Here's a very interesting propaganda poster from Britain published in 1793: https://imgur.com/a/vYxHEM3