There's this passage in Dorothy L. Sayers' "Busman's Honeymoon" (published 1937, set in England), from a letter written by an old Countess:
Not that many marriages can be called permanent these days, but I can't see Peter [Lord Peter Wimsey, who's about to finally get married] exhibiting himself in the Divorce Courts for his own amusement, though, no doubt, if asked to oblige, he would carry it through with an air.
(Which reminds me that my idiot great-nephew, Hughie, has bungled matters as usual. Having undertaken to do the thing like a gentleman, he sneaked off to Brighton with a hired nobody, and the Judge wouldn't believe either the hotel bills or the chambermaid—knowing them all too well by sight. So it means starting all over again from the beginning.)
So, as I read this, Hughie and his wife want to divorce, and "like a gentleman" Hughie is willing to take the blame. He stages a romantic getaway to the seaside with a "hired nobody", in which he is to be caught complete with a witness and written proof, so they can be divorced due to his supposed infidelity. But the judge seems to be familiar with this kind of ploy, and the attempt fails.
Which leads me to asking: Was this actually something people (and people of the upper class, too) did, being willing to be bear the public stigma of infidelity in order to be able to dissolve a marriage? Were there sensational cases of this sort, where the attempt succeeded or failed? Was there public discourse about them? Would Hughie or his wife be snubbed by their peers if they had managed to carry the scheme through?
I'm asking mostly about the setting of the novel, that is England around the 1930s, but of course similar cases from other places and times with a similar legal framework would also be interesting.
And please, if you have literature I can read about this sort of thing, do tell me! I'm not scared of academic literature, footnotes and all, in German or English.
Your big source is going to be the various documents produced by Royal Commission on Marriage and Divorce 1956. Getting hold of them might be a challange though.
But yes what you describe was common enough to support an industry of private investigators who sat outside hotel rooms.
There are however some complications. Firstly the affair might not be fake. You'd have a couple who had separated for years and had shacked up with other people but in order to sort the paperwork out one of them would generally have to hire a private detectives, to watch them go into a hotel room with their partner.
The year 1937 is also important that's the year the Matrimonial Causes Act 1937 passed. Prior to that it would take more than plain adultery on the part of the man to get a divorce (plain adultery on the part of the woman would qualify). Hughie would have had to admit to some level of domestic violence or the like as well to do the honourable thing before 1937.
There is also the issue that in the case of a fake affair there would be a bunch of perjury going on. Everyone involved understood this of course but the issue is still there.