Wikipedia says, without citation, that C. S. Lewis's novel That Hideous Strength was "heavily influenced by the writing of Lewis's friend and fellow Inkling Charles Williams". I did notice that this novel seems different in style from Lewis's other work that I've read (Narnia, Till We Have Faces, and even the other novels of his Space Trilogy): it's much more grounded and down-to-earth, set in our own modern world, its sci-fi/fantasy elements much less obtrusive into the very setting of the story. But, not having read any Charles Williams, I didn't realise that this style difference was due to influence from another author.
What is the evidence for Charles Williams having influenced That Hideous Strength? Did Lewis explicitly say so, as he did acknowledge influence from Olaf Stapledon in the preface? Is it purely based on analysis of the book by critics? Or is there some other evidence e.g. from contemporaneous Inklings meetings?