... with whom?A long shot, but I would say 1871.
By Prussia?
... with whom?
The Germans?
They had a heck of an army, sure, but what navy?
I make it that they had five ironclads, as opposed to the RN which had at the time about thirty-three. Plus eight coastal ironclads designed to take the fight directly to the enemy's harbours, and another six ironclads commissioned in 1871!
I would say the last best opportunity would be during the Seven Years War, by France. This is the last time that a Rival Great Power to Britain had a Navy to invade with, and, with a small PoD, the diplomatic freedom to commit their resources and focus to such an invasion.
France... having just been hammered flat by the Prussians?No by France.
http://dossiersmarine.free.fr/index.html
1871 was when France stopped trying to have a meaningful navy and concentrated wholly on the army. Until then, the French Navy was often within shouting distance of the RN and it was possible (even if not likely most of the time) that the French Navy, with luck, could dominate the RN enough to allow an invasion of England. In particular, the 2nd Empire was one of the few times in history when the French Navy was arguably, for some little time windows (e.g. 1863), superior to the RN. After that, the MN was not even in the same league as the RN (discouting late 20th, early 21st century, of course).
When was the last time another nation had the navy to beat and then invade the British isles before 1900 and after the HYW, and how succesful would they be when they landed.
France... having just been hammered flat by the Prussians?
Huh, I assume you're using an earlier PoD then.
I mean in a TL in which they are not at war with the prussians, of course (or they win the war). My point is that the MN was the last power which rivalled the RN before the 20th century and France turned from it after 1871 OTL. So the last time OTL anyone could have invaded England (with even a little chance of success) before the 20th century was 1871. AFterward you have to wait until WWII.
Wait, who in 1871 could have invaded Britain? Wasn't the British Navy more than twice the size of the French Navy at the time?
No, most definitely not. Check the link I posted upthread.
..would you happen to have a link in English?
EDIT: And maybe twice the size was a bit of an exaggeration, but I was under the impression that British naval supremacy was basically unchallenged between 1814 and 1880. And even after that, when Germany tried to compete, it never really came close.
SECOND EDIT: I found a list of warships launched by each country between 1850 and 1870. France built 26 cruisers, the United Kingdom built 62. France built 20 battleships, the United Kingdom built 40, including the HMS Hotspur (I guess somebody in the Royal Navy was a Tottenham fan).