(Repost as it didn't get much attention last time) Anecdotally, my father -- a history major -- claimed that the British in speeches, writings and more from both public officials and the general public such as newspapers, entertained a sentiment of retaking the United States or adding them back to the British Empire. He further claims that when British military observers relayed the state of the United States armed forces at the end of the Civil War (with more than a million men under arms) that all such sentiment vanishes from the British. My own, limited, research doesn't really turn anything up on this beyond the Trent Affair. So I have three questions:
The titular question: Did the British ever entertain a revanchist sentiment toward the "lost" American colonies?
If so, when did such sentiment end and what was the cause?
Were there British observers of the American Civil War and what were their thoughts throughout the war?
Any suggestions for further reading on this topic would be greatly appreciated as well!
Follow up question: Did any of the other major countries (Spain, Portugal, probably not France) consider taking the US after the UK lost them?
There is always more that can be said here, but we have had some similar questions in the past. I would point to this answer from /u/partymoses touching on it, while this thread looks at changes to Anglo-American relations, as does this one although it is a bit older.
Britain never considered retaking all of the United States, and the most they ever entertained was dividing it (supporting the Confederacy, a plan which never happened) and blocking its growth (forts along the Ohio River Valley, using Canada to block northern growth, and fighting over areas like Oregon). Even if animosity continued between Britain and America until the 20th century, the biggest escalation of it was the War of 1812, which never had the end goal of returning America to the fold.
The fact is that immediately after the American Revolution, Britain was still economically controlling the U.S- under the Articles of Confederation, Congress couldn't pass tariff laws, and so British goods flooded the American market. All in all, Britain was still profiting off their old colonies, at least until the Constitution was signed. By that point, the French Revolution was stirring, and Britain's attention had long returned to Europe.
Because America had decided on being an isolationist and neutral country, they did nothing to help the French Revolution. Britain could care less about them at this point, besides problems in the Ohio River Valley with old military forts, and Jay's Treaty gave them everything they wanted, so they pretty much just backed away.
Of course, the War of 1812 did bring British attention back to America, but it wasn't to retake the US, merely to force them to trade. This was because of Jefferson's embargo on both Britain and France, eventually letting it up on France and only focusing on Britain. After America's respectable showing in the War of 1812, Britain and the rest of Europe understood that the old thirteen colonies were now a respected country, so at this point any talk of taking them back was naught.
TLDR: No, they did not consider taking America back, and even if they did they never took actions to implement such a plan besides annoying America in the West.