Oh gosh, the 18th century was a time of political drama, celebrity, notoriety, infamy, and serious accomplishment, all mixed together. I find it, politically speaking, the most interesting period of history.
Of course both Pitt the Elder and Pitt the Younger overshadow some parts of the eighteenth century and are certainly giants when we consider narratives of war and conflict. But there are some other giants, too.
Robert Walpole is generally considered the 'first' prime minister. He would certainly be my choice on any poll. As a whig politician, his career began in 1701, having served both George I and George II, in 1721 he became First Lord of the Treasury after being seen as the saviour who would rescue Britain from the South Sea Bubble. But it was not until 1730, with the retirement of Lord Townshend, when he became undisputed leader of the Whigs and managed British politicals almost unchallenged until 1742, when the War of Jenkins' Ear (or War of Austrian Succession, as it would become) was not being executed as successfully as hoped. Walpole's biggest achievement was to keep Great Britain at peace for almost 2 decades, allowing her to become far more prosperous and commercial, after the destructive (though overwhelmingly successful) War of Spanish Succession.
So yes, definitely Walpole for my choice.
Others would be :
Charles Townshend
Duke of Newcastle
Henry Pelham
Thanks,