[Update: after posting this, I was informed (see comments) that Frank Cioffi had died the previous day. It seems fitting, in acknowledgement of this strange coincidence, to dedicate this post, humble as it is, to his memory. He helped us to think through our loneliness to the end. May he rest in peace.]
I just occurred to me that I might have been remembering the quote wrong. Sure enough, I've now located it in a book I read many years ago. In his contribution to The Impulse to Philosophize, "Congenital Transcendentalism and 'the loneliness which is the truth about things'", Frank Cioffi writes:
I take the phrase ‘congenital transcendentalism’ from Santayana who defined it as ‘the spontaneous feeling that life is a dream’. ‘The loneliness which is the truth about things’ is a phrase of Virginia Woolf's. The thesis I will advance is that many expressions of doubt or denial of the shareable world are self-misunderstood manifestations of the state indicated by Woolf's expression. But the loneliness of which Woolf speaks must not be construed as the kind of loneliness which can be assuaged by family, friends, lovers or company. Nor is it the loneliness which a convinced solipsist might experience. It is rather the loneliness of ‘that “I” and that “life of mine’” which is ‘untouched whichever way the issue is decided whether the world is or is not’ (Husserl, 1970, 9).
He concludes the same essay by saying that Woolf's phrase sums up "the unique ontological structure of being" (p., 138).
We can easily construct supplements: "the friendship which is justice among people", "the common ethnographic texture of becoming" (clear, no?). I like the idea of a loneliness that brings us closer to truth just as much as I like the idea of a friendship that brings us closer to justice. Naturally, both experiences can be perverted and succumb to illusion.
Update: I probably read it in Cioffi's Wittgenstein on Freud and Frazer. But Cioffi does not provide a reference and I have still not been able to locate the phrase in Woolf's writings.