Here is a summary of the major reasons why I believe this is certain and not merely possible:
First, Manning was a major Janeite. As evidence of same, I give you the following quotes from the 2013 literary bio, Olivia Manning: A Woman at War by Deirdre David:
P. 169: “ [In 1945, Manning declared] ‘JA should be re-read at least every two years, and even more frequently as one ages, sine she gives ‘a truer picture of human nature than the wicked Mr. [Oscar] Wilde could ever do.’ ”
P. 204: “[Manning agreed] with Francis King that JA ‘really had no conception of what men talked about when they were away from women….”
P. 301-2: “…all this talk about ‘morality’ and adult responsibility hardly accords with the droll skepticism we associate with Olivia Manning’s fiction. These emphases, however, inform an introduction Olivia wrote in 1968 for a Pan Books edition of JA’s NA. Taking a break from writing The Play Room, she praises Austen’s strict moral sense, declaring that ‘her concern with kindness, honesty, reason, and right conduct, inform her novels with a goodness that we recognize as moral inspiration.’ If we read TPR as in some sense a moral fiction, then it would appear that Olivia intended this novel about sexual perversity and violence to expose a world quite distinctly NOT ruled by [those 4 things]. In NA, the heroine discovers…that the true villainy in the world lies in schemes of arranged marriage, financial settlements, and advantageous alliances. In TPR, Laura discovers that her sexual fantasies about Vicky Logan are nothing compared to the graphic violence that she sees has been executed upon her languorous body. “
Second, I have previously posted on several occasions about the veiled but significant allusion to Troilus and Cressida in Mansfield Park, including but not limited to the following posts:
So it seems clear to me that Olivia Manning picked up on that same allusion to T&C in MP, and demonstrated this in an Austenian way, by a complex but veiled allusion to MP in Fortunes of Law in which she brought Troilus & Cressida to the overt level, and submerged Lovers’ Vows (as to which, she made one subtle wink, with the name she gives to one of the characters who plays a role in Troilus & Cressida: Inchcape (which sounds an awful lot like Inchbald, whose translation of Lovers Vows was used by JA in MP).
But the above is only the beginning of Manning’s covert allusions to JA. While it would be too complicated to explain here and now, suffice to say that two of Manning’s later novels also owe a great deal to Mansfield Park:
The Play Room (which was discussed by Deirdre David in the quotation, above) and The Doves of Venus are both strongly resonant of the relationship between Fanny Price and Mary Crawford, in particular the suggestions of more than a platonic connection between two young women. Turns out that Olivia Manning herself was from the other side of the tracks in Portsmouth, and that these two late novels of hers were both highly autobiographical.
Manning saw beneath the surface of JA’s novels, and was apparently particularly drawn to the dark, unwholesome moral murkiness of MP, with regard to sexuality as well as colonialism and war.
Which is why Troilus & Cressida, which is all about those same themes, was chosen by JA as an allusive source for MP, and why Manning chose both MP and T&C as allusive sources in her own fiction. In particular, the emphasis given in the Fortunes of War of the scenes between (uncle) Pandarus and (nice) Cressida shows me that Manning picked up on exactly the creepy quality of the relationship between Fanny Price and her uncle, Sir Thomas Bertram, in MP.
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