Who was the first British Prime Minister to regularly wear long trousers instead of knee breeches?

The picture is of Charles Watson-Wentworth (1730–1782), Second Marquis of Rockingham; it shows how British Prime Ministers used to look.

The 1768 portrait by Joshua Reynolds gives us a partial view of what the Prime Minister is wearing from his waist down to his knees. These wonderful breeches would be fastened about his legs by buttons, drawstrings and brooches. Breeches of various types were standard items in men's wardrobes during Lord Rockingham’s time -- he was Prime Minister in 1765-1766 and again in 1782 – but they had fallen out of use by the mid-19th century. In came trousers.

Now to the answer options.

On the prime-ministerial timeline William Pitt the Younger (1759-1806) and Spencer Perceval (1762-1812) would have been breeches men like Lord Rockingham; but the Duke of Wellington (1769-1852), who served briefly as Prime Minister in 1834, was definitely in the trousers era.

The pivotal person here is Robert Banks Jenkinson, 2nd Earl of Liverpool (1770-1828) who was a remarkable Prime Minister. He was in office from 1812 to 1827, a total of 14 years and 305 days, making him the longest-serving Prime Minister from the mid-18th century to the present day (2021). Liverpool dealt with the constitutional issues raised by the regency during the period in which King George III was incapacitated. He steered the country through the period of radicalism and unrest that followed the Napoleonic Wars. He was also the first trouser-wearing Prime Minister.