Reading 'The Man Whom the Trees Loved' by Algernon Blackwood, I find myself wondering if this is a case of parallel evolution, or whether JRRT was influenced by this material in working up the Ents. Are there any notes that indicate that he was aware of this story?
There is no mention of Algernon Blackwood in the Letters, and neither in the HoME, Unfinished Tales or The Silmarillion. Tolkien seems to suggest that the main inspiration for the Ents would've been George MacDonald's walking tree spirits (if there was any significant inspiration) with the idea of them going to war taken from Shakespeare's Macbeth. Shakespeare, however, did not inspire them as a character but motivated their actions (marching to war).
Tolkien himself was never sure of interpretations to his work, and "found it amusing" to find interpretations:
The Lord of the Rings as a story was finished so long ago now that I can take a largely impersonal view of it, and find 'interpretations' quite amusing; even those that I might make myself, which are mostly post scriptum: I had very little particular, conscious, intellectual, intention in mind at any point.
The Letters of J.R.R. Tolkien: Letter 163
This quote is followed by note 41 of the Letter (On the topic of Ents):
Their part in the story is due, I think, to my bitter disappointment and disgust from schooldays with the shabby use made in Shakespeare of the coming of 'Great Birnam wood to high Dunsinane hill': I longed to devise a setting in which the trees might really march to war.
The Letters of J.R.R. Tolkien: Letter 163, Note 41
This seems to suggest that in 1955, Tolkien was aware of the influence of Shakespeare's Macbeth on the storyline of the Ents, however does not credit Shakespeare with inspiring their invention.
From an unpublished letter dated 1958, Tolkien claimed that the Ents were "original" and describes their inspiration from his life, but admits to influences from George MacDonald's and again Shakespeare's Macbeth:
Ents is also an ancient English word (for a giant); but the Ent of my world I suppose are entirely "original" creatures, so far as that can be said of any human work. If you like, they are a mythological form taken by my life long love for trees, with perhaps some remote influence from George MacDonald's Phantastes (a work I do not much like), and certainly a strong (twist?) given my deep disappointment with Shakespeare's MacBeth...
From a letter to Mrs LM Cutts
In it's original form
In 1956 and again in 1963, Tolkien seems to suggest that his Ents simply came to him and that he had "no recollection of inventing" them. Suggesting that during the writing of Chapter IV of Book Three, the story created the characters itself. Although admitted to knowing that Frodo (even though it turned out to be Merry and Pippin) would have a tree-adventure.
Thus, though I knew for years that Frodo would run into a tree-adventure somewhere far down the Great River, I have no recollection of inventing Ents. I came at last to the point, and wrote the 'Treebeard' chapter without any recollection of any previous thought: just as it now is. And then I saw that, of course, it had not happened to Frodo at all.
The Letters of J.R.R. Tolkien: Letter 180
There are or were no Ents in the older stories – because the Ents in fact only presented themselves to my sight, without premeditation or any previous conscious knowledge, when I came to Chapter IV of Book Three.
The Letters of J.R.R. Tolkien: Letter 247
Tolkien himself described the process (or as much as he consciously can make of it) in a footnote to Letter 163:
Take the Ents, for instance. I did not consciously invent them at all. The chapter called 'Treebeard', from Treebeard's first remark on p. 66, was written off more or less as it stands, with an effect on my self (except for labour pains) almost like reading some one else's work. And I like Ents now because they do not seem to have anything to do with me. I daresay something had been going on in the 'unconscious' for some time, and that accounts for my feeling throughout, especially when stuck, that I was not inventing but reporting (imperfectly) and had at times to wait till 'what really happened' came through. But looking back analytically I should say that Ents are composed of philology, literature, and life. They owe their name to the eald enta geweorc of Anglo-Saxon, and their connexion with stone. Their part in the story is due, I think, to my bitter disappointment and disgust from schooldays with the shabby use made in Shakespeare of the coming of 'Great Birnam wood to high Dunsinane hill': I longed to devise a setting in which the trees might really march to war. And into this has crept a mere piece of experience, the difference of the 'male' and 'female' attitude to wild things, the difference between unpossessive love and gardening.
So, probably not influenced by Algernon Blackwood, though possibly by Shakespeare.