A more powerful monarchy probably requires a more authoritarian Britain generally; perhaps a spin on the old 'King Ernst Augustus' idea? Normally that's used to give rise to a revolutionary Britain, but if we generally encourage the worst aspects of British authoritarianism in the early nineteenth century- let's say a surviving French Republic and some sort of British loss in the resulting wars means that the siege mentality that pervaded much of the establishment's thinking persists. You see the same general increase in heavy handed policing; the old saw about how violence in an empire is eventually brought home to the metropole could be another useful way of ratcheting up the oppression. Say there's another severe rising in Ireland in the 1820s* which leads to more repression in the booming cities generally, which means more hanging and transportation of radicals.
This all encourages hostility to reform acts, and you see an authoritarian parliament backed- ideally- by a conservative monarch. By the 1830s, there's probably been widespread unrest, but as 48 shows us that doesn't need to lead to actual reform. The reactionary state could persist. In fact, Ernst probably isn't needed- I think that the young Victoria would be perfectly aligned in temperament and politics with this sort of thing.
The tricky thing is how to do this without leading to a republic.
Let's say that the Reform Acts do eventually begin to be passed- but decades behind schedule. Eventually some British Bismarck figure (Disraeli's the most obvious, but probably he wouldn't rise in this environment, what with Not Being the Right Sort) realises that they can try to channel the change or be swept away by it, and you see some great speeches about constitutional reform.
The result is a Britain that's something similar to the Second Reich- lots of nominal democracy, but still massively dominated by landowners, with a great deal of power vested in the crown.
This isn't convincing me, to be honest; after 1688 I tend to think that an authoritarian, traditionalist Britain would see power stay in the hands of the Lords, not the Crown. That's not just a matter of actual practical politics- by then, even the right wing had invested a great deal of their mythology in the idea of parliament, not the monarchy, being the source of authority.
*I swear to god that I'm not trying to open that can of worms again, I just think it would be more traumatic than a loss in India in the 1820s would be.