Sterling was unruffled, with the UK currency drifting 0.1% lower on the day. Government bond pricing showed barely a whisper of concern.
Investors said developments since Scotland voted by a 55% majority to remain in the union in 2014 have made this potential market driver much weaker than it once was.
"Ten years ago it was a real risk, it was quite close," said Jon Day, global bond portfolio manager at UK-based asset manager Newton Investment Management.
Since then, Day pointed out, "politically there's no will in Westminster to hold another referendum."
Last November, the UK's top court ruled Scotland could not hold another independence vote without Westminster's approval. The ruling Conservative Party is committed to maintaining the union with Scotland, while opposition leader Keir Starmer wants to hand more power to UK regions but is more focused on reconnecting Britain with Europe. Sterling one-month volatility, a measure of short-term swings in the currency, spiked during the 2014 referendum but traded calmly on Wednesday and Thursday. The domestically focused FTSE 250 share index drifted 0.2% higher on Thursday, while the yield on the 10-year UK gilt , a benchmark for the UK government's borrowing costs, inched 2 bps lower. The Scottish independence discourse "doesn't have much of an impact on the pound these days", said George Brown, economist at fund manager Schroders.
The proportion of Scots who support independence has remained steady, with polls still indicating an even split. Markets also "in general have a dreadful tendency to focus on only one thing", Newton's Day said. And at the moment, the outlook for inflation and central banks' interest rate decisions are strongly overshadowing political risks for investors the world over.
"The impact of geopolitical risk on markets has been muted," said Tina Fordham, founder of independent risk consultancy Fordham Global Foresight, as "central bank liquidity has provided a kind of dampening effect" on market perceptions of political risks.
Such risks may become more acute as global monetary policymakers remain hawkish. The U.K. market chaos following former Prime Minister Liz Truss's badly received mini-budget collided with heightened anxiety among investors in general as the U.S. Fed raised interest rates.
For now, however, markets will at most "be wanting to see," who replaces Sturgeon before taking any view on the prospect of another Scottish independence vote, Equiti Capital macro economist Stuart Cole said.
"If she is replaced by another pro-independence leader who will likely put renewed energy into the push for a referendum, then that is potentially negative for sterling," Cole said (Reporting by Naomi Rovnick; Editing by Amanda Cooper and Nick Macfie)