I sense that all of these are in the ASB thread.
I'll take your word for it. I was just picking ASB examples as they occurred to me.
I do agree with the general idea (that Wellington would never have deposed the legitimate monarchy so the OP needs some other connivance to be achieved), but…
(a) The British ships of the line that fought at Trafalgar weren't the only ships of the line in the Royal Navy, and not all naval victories in history (indeed, few of them) are as decisive as OTL's Battle of Trafalgar. France wins at Trafalgar =/= Napoleon successfully invades Great Britain. The latter is much more difficult than the former.
(b) So Napoleon is clearly on the road to defeat (thank you Russia), the Hanoverians have the opportunity to take the throne of a country clearly destined for resurgence (simply as a function of Napoleon's defeat), and instead, unlike OTL where almost every monarch in Europe jumped at the chance to join in against Napoleon and see what they could get, they choose to cower in Hanover, which is far more vulnerable to Napoleon than Great Britain is anyway. Right.
The reason this is so unlikely is because Britain had already had a military dictatorship in the seventeenth century and they didn't like it. You could say that the interplay between politics and the military since then was designed to prevent Wellington or someone like him from staging a Coup d'état.
A perceptive point in regard to Cromwell, and I agree, with one caveat: Wellington was absolutely not the sort to launch a
coup d'état. He was a staunch traditionalist, a man of strong principles and a man with a strong respect for the rule of law and a willingness to let it limit his own ambition. He was the last person on Earth who might be expected to overthrow the established government, especially out of any personal ambition. The way certain TLs describe Wellington, one might think that their authors are confusing him with Napoleon, perhaps because they were both famous, skilled Napoleonic-era generals with nice coats…