The following snippets are taken from Google Books:
1.1 Lindsay Roy: I would have thought the status quo is the position that they retain. Is that not a reasonable assumption?
Professor Scott: I do not think so, but you are welcome to hold it. I do not hold it.
1.2 Chair: I ask because we will obviously want to pursue with the Scottish Government at some point the question of the 20-year figure. If that is deemed by people, including the Defence Academy, to be a reasonable figure for moving. we will then want to clarify with them whether or not they are prepared to allow Trident 20 years until such time as replacements are built.
Peter Luff: Chairman, I would have thought you would also need a period of consultation with the local population where you are moving it to. It would be a very long project indeed.
1.3 "I would have thought that it is not likely to build peace and harmony. Can you see anything other than the full 20 years as being conducive to an agreeable settlement"?
1.4 "I can see that if you want to have expeditionary forces. they would be valuable, but I would have thought that in those circumstances the bigger forces would have surplus capacity and that they would be working harder."
The Referendum on Separation for Scotland, Session 2012-13: Oral and Written Evidence
2. I would like to make two suggestions: one element which I would have thought the Minister would have included, if not in his actual speech, in his "background thinking" is the business of land adjudication. My hon. friend is looking at me with very keen eyes and I hope that he is going to understand what I am talking about.
Kenya National Assembly Official Record
3. The youngest of his children was just left school. I had seen it in the Press. She had passed high up in her exams at the school at Beaucamps, and was going to be an air-hostess. I couldn’t see what she wanted all that education for to be an air-hostess. I would have thought all she needed was to know how to smile.
The Book of Ebenezer le Page by G.B. Edwards
4. In the process of climbing the brick with the spider in tow, the wasp slipped and lost its grasp, falling to the ground. You would have thought that by now, the wasp would have become frustrated and decide to give up, but to the contrary the wasp grabbed the spider and continued its task.
By the Grace of God: Accompanied by “Shadows and Reflections” by James R. Read
As FumbleFingers points out, (primarily of UK speakers) people often say I'd have thought when what they really mean is I think. It's just a kind of "distancing circumlocution" that often conveys more a sense of polite deference, rather than hesitant uncertainty or conditionality. Plus, of course, standard principles of sarcasm mean it can be used witheringly/haughtily.
Example 1.1 - 1.4 and 2. can serve as examples of such use, but example 3. and 4. are somewhat different.
Would a non-BrE speaker be able to identify the subtle nuance?
Ordinarily an subordinate clause is expressed with the same tense and mood as the main clause.
However, as we can see, some of these examples appear to violate the sequencing rule. In these contexts, tense or mood is just a stylistic choice?