Well it's a half-solution but apparently around the end of the Napoleonic Wars there was a fear that the British were becoming so powerful that they would form a permanent European "summit" (of sorts) where they would settle all issues and prevent conflicts, using their naval and economic strength to pressure combatants to withdraw from wars. Since the British had no real continental ambitions - where just about every other major European country did - this therefore gave them somewhat of a feeling of moral supremacy. It would operate a bit like a modern-day UN I guess, only with one nation overwhelmingly dominant acting as arbiter and dispatcher of justice, and not afraid to use its own armed forces to smack down aggressors. Maybe if you have the ARW failing you could have the UK dominant enough to achieve this - and maybe slightly tinker the Napoleonic Wars to balance the surviving countries - a more peaceful and acceptable solution to "the Saxony question", have Russia take some infrastructural damage from the 1812 invasion so it doesn't feel ready to try seizing the Bosphorus, etc. Then you just need the UK and the other colonial nations to gobble up the remaining non-European countries to turn them into colonies and you have the entire world under one authoritative presence.
It's speculation, of course - there's no evidence OTL that the UK ever wanted to do such a thing. But it serves its purpose here.