Did the use of the term Prime Minister in the UK originate as ridicule?

Yes, according to the British government itself:

The title ‘prime minister’ was originally a term of abuse rather than a description of an official role. It implied that an individual subject had risen improperly above others within the royal circle, and had echoes of a political institution imported from France, England’s great enemy. When Robert Harley, a favourite of Queen Anne (1702-1714), was impeached in 1715, one of the charges against him was that he was a prime minister.

Walpole himself felt it necessary to deny the accusation, as that page quotes:

“I unequivocally deny that I am sole and prime minister.”

I recommend Iain Dale, The Prime Ministers: Three Hundred Years of Political Leadership, with short portraits of the PMs from Robert Walpole up to Boris Johnson. Very nice if you are into this sort of political-historical nerdery.

From the introductory chapter "The Office of Prime Minister in History" by Andrew Blick:

In the early eighteenth century, by contrast, the post had no official existence. Furthermore, to describe someone as a 'prime minister' was a way of attacking them. The term implied a subject of the monarch who had obtained too much power. According to received wisdom at the time, the different royal ministers were equal in their responsibility to the ruler. As a phrase, it also had French connotations, suggesting the undesirable incorporation of the methods of a foreign, rival power and tyrannical political system into our own. During this time as First Lord of the Treasury between 1721 and 1742, when accused of being a prime minister, Walpole disputed this claim. As he put it to the House of Commons in 1741: 'I unequivocally deny that I am sole and prime minister.'

It would be more like an accusation than ridicule, but meaning of the word prime and the circumstance of the accusation's use are not easily understood in modern culture.

The word 'prime' denoted more than the ordinal, e.g. the first of some number of equals. Prime identified a root from which all others of that kind had grown. It invoked the primogenitor, the male head of the family. The styling of one minister as 'prime' now refers to a modern power conferred on the prime minister by the crown to form a government by inviting others to serve with the prime minister. The older use of the word was more literal.

The 18th century accusation had its roots in the religious tumult of the Tudor dynasty that ultimately led to the English Civil War and the eventual restoration of a weakened monarchy. The accusation picked at the scab of a wound that would not heal until the 19th century.

During the reign of Elizabeth I she was vigilant to avoid the cultural bias that assumed that a married woman would cede control to a husband to bear children and raise them to adulthood. A corollary assumption was that a woman who relied on a single principle advisor would in the natural course of events come to assume the remaining attributes of a married woman. The religious schism that Elizabeth finessed with the phrase "I will not create windows into men's souls" would not survive a marriage, every man was identified with one faction or the other. Elizabeth was compelled to dispose of romantic interests and depose favored advisors whenever the specter of a controlling male incited factional division.

By the mid 19th century the religious schism no longer signified factions struggling for ascendance and the powers that the monarch would and would not choose to exercise were comfortably settled to proscribe capricious alterations to the status of the great and powerful. Victoria, unlike any of her ancestors, retained sovereignty in whole when she married a foreigner Albert, styled prince and consort, had a large family and a long reign. Elizabeth II's choice of a foreign prince and her long reign may or may not signal a pattern that will eventually be repeated.