But with the debate over Scottish independence now hurtling towards a climax, the timing is more than a little awkward.
The man immortalized atop the plinth, resplendent and seated on horseback, is Prince William Augustus, Duke of Cumberland, the youngest son of Britain’s King George II and "Sweet William" to his supporters.
But he inhabits a darker place in history for many Scots, who know him as “the Butcher of Culloden.”
Not content to merely put down the last Jacobite uprising at the battle of Culloden in 1746, Cumberland hunted down and ordered killed all the Scottish Highlanders who’d dared to support Bonnie Prince Charlie’s doomed claim to the throne.
“For a lot of Scots it does represent a very troubled period in the relationship between England and Scotland,” says Laura Stewart, a professor of British history at the University of London.
"It’s the point at which many Scottish elites, in the middle of the eighteenth century, understand that there is only one game in town, and it’s the union.”
A key battle for the British state
The Battle of Culloden came some 40 years after the Acts of Union bound the English and Scottish kingdoms.
“From a British perspective, this is a battle that confirmed the military primacy of the British state. Its ability to control its own people, within its own territory,” says Stewart.
But the Duke’s methods were deemed so brutal, even in London, that the statue was actually removed from the plinth in 1868.
So why, after all these years, has it been returned to pride of place, to sit basking amid Londoners out eating packed lunches on the grass on those rare days when the sun is shining?
The statue is actually an art installation by the South Korean artist Meekyoung Shin. Her web site describes “Written in Soap: A Plinth Project” as a comment on "the mutable meanings” we attach to history.
The Westminster Council, which approved the project, refused to comment.
The sculpture is not supposed to last, the idea being that it will slowly release a fragrance as the statue decays and crumbles.
“'Butcher’ Duke raises a Stink in the Highlands” was the headline in the newspaper The Scotsman when the statue was first unveiled in July 2012 for what was to have been just a year on the plinth.
But it’s still there, the cracks and fissures that crisscross its surfaces deepening with each passing day, a good metaphor for the fault lines that may be left behind after Thursday’s referendum.
Differing historical views
Interpretations of history are certainly playing an important role in the rival campaigns to convince Scottish voters either to go it alone or remain in the embrace of the Union.
Stewart points out that many in Scotland did not support the Jacobite uprising and were happy to see it suppressed.
But some of the issues at the heart of that struggle, of course, are the same as those being aired in the course of the independence debate.
As is so often the case in the realm of history, the narrative can be molded to please both sides, says Stewart.
“Obviously for the Yes campaign, they want to say there’s a coherent nation — the Scots, the Scottish people — who have some sort of claim to national self-determination.
“For the Better Together [or No] people, what they want to say is that despite the different variations within the British state, we are better together because we have a shared history.”
So how will history judge Thursday’s vote? And how long will it take for hard lines to soften and fade again?