Colin Wilson's book The Strength to Dream: Literature and the Imagination (which you found) has an entire chapter entitled "The Assault on Rationality", in which Lovecraft features prominently as one of the authors discussed. Wilson takes a very dim view of Lovecraft and his writing (and I quote: "it must be admitted that Lovecraft is a very bad writer"), but here are some passages which summarise the idea you're looking for:
Lovecraft is interesting mainly because he is a perfect example of the "escapist imagination". It is hard to agree with August Derleth that his death was "a great loss to American letters" because he had not yet reached "the fullest development of his powers." It is doubtful whether Lovecraft had any more to say. As it is, he wrote far too much. Moreover, since he so determinedly created an unreal world in opposition to the real world, it seems that he willed his own death. His whole life is a spectacle of self-destruction; he strikes one as being like a chronic alcoholic or a drug addict.
For this reason, it is interesting to compare him with W. B. Yeats. We tend to think of Yeats as a combination of poet and politician; he has been compared to the older Goethe. And yet Yeats, like Lovecraft, created his own world of myths and symbols, and tried to force it upon the "real world."
-- pp. 10-11
Lovecraft did his best to convince the reader of the reality of his unseen world, but he never asserted in print that he had seen Cthulhu. Yeats's extraordinary attack on the "materialistic world" reached a climax in a strange book called A Vision.
-- p. 13
Wilde epitomises the imagination as "escapism". Yeats and Lovecraft set up the imagination as a faculty for challenging and defying the "real world"; but Wilde carried the defiance to the point of suicide. For these writers, the imagination was essentially the alternative to reality.
-- p. 20
All bold emphasis mine in the above quotes. The book is available on the Internat Archive for borrowing.
Although the phrase "assault on rationality" does not literally appear in the same sentence as the word "Lovecraft", the lengthy discussion of Lovecraft's approach to writing in a chapter entitled "The Assault on Rationality" is enough to make the connection.
For further reading, there are other sources predating Wilson, but at least one of them may be harder to track down:
The following facts are taken from August Derleth's H. P. L.: A Memoir. I would like also to acknowledge Mr. Derleth's help in providing me with additional information about Lovecraft. My other chief source of information has been J. Warren Thomas's unpublished hesis on Lovecraft, which I consulted in the John Hay Library of Brown University, Providence, R. I.
-- p. 2