There is direct evidence of this, and since the question is not a new one, nor infrequent to those doing scholarly work, research or thesis papers, I think the evidence should be put forth here for all future inquiries.
So, this will be a long post, but if you aren't interested in Chesterton's influence on Gandhi, you can skip this by not clicking here.
In his Illustrated London News column on September 18, 1909 (Oct. 2 – American edition), Chesterton wrote the following:
It is this lack of atmosphere that always embarrasses me when my friends come and tell me about the movement of Indian Nationalism. I do not doubt for a moment that the young idealists who ask for Indian independence are very fine fellows; most young idealists are fine fellows. I do not doubt for an instant that many of our Imperial officials are stupid and oppressive; most Imperial officials are stupid and oppressive. But when I am confronted with the actual papers and statements of the Indian Nationalists I feel much more dubious, and, to tell the truth, a little bored. The principal weakness of Indian Nationalism seems to be that it is not very Indian and not very national. It is all about Herbert Spencer and Heaven knows what. What is the good of the Indian national spirit if it cannot protect its people from Herbert Spencer? I am not fond of the philosophy of Buddhism; but it is not so shallow as Spencer's philosophy; it has real ideas of its own. One of the papers, I understand, is called the Indian Sociologist. What are the young men of India doing that they allow such an animal as a sociologist to pollute their ancient villages and poison their kindly homes?According to P.N. Furbank (“Chesterton the Edwardian,” G.K. Chesterton: A Centenary Appraisal. John Sullivan, ed., Harper and Row, 1974)ISBN 13: 9780236176281 & ISBN 10: 0236176285, Gandhi was “thunderstruck” when he read this article.
When all is said, there is a national distinction between a people asking for its own ancient life and a people asking for things that have been wholly invented by somebody else. There is a difference between a conquered people demanding its own institutions and the same people demanding the institutions of the conqueror. Suppose an Indian said: "I heartily wish India had always been free from white men and all their works. Every system has its sins: and we prefer our own. There would have been dynastic wars; but I prefer dying in battle to dying in hospital. There would have been despotism; but I prefer one king whom I hardly ever see to a hundred kings regulating my diet and my children. There would have been pestilence; but I would sooner die of the plague than die of toil and vexation in order to avoid the plague. There would have been religious differences dangerous to public peace; but I think religion more important than peace. Life is very short; a man must live somehow and die somewhere; the amount of bodily comfort a peasant gets under your best Republic is not so much more than mine. If you do not like our sort of spiritual comfort, we never asked you to. Go, and leave us with it." Suppose an Indian said that, I should call him an Indian Nationalist, or, at least, an authentic Indian, and I think it would be very hard to answer him. But the Indian Nationalists whose works I have read simply say with ever-increasing excitability, "Give me a ballot-box. Provide me with a Ministerial dispatch-box. Hand me over the Lord Chancellor's wig. I have a natural right to be Prime Minister. I have a heaven-born claim to introduce a Budget. My soul is starved if I am excluded from the Editorship of the Daily Mail," or words to that effect.
Now this, I think, is not so difficult to answer. The most sympathetic person is tempted to cry plaintively, "But, hang it all, my excellent Oriental (may your shadow never grow less), we invented all these things. If they are so very good as you make out, you owe it to us that you have ever heard of them. If they are indeed natural rights, you would never even have thought of your natural rights but for us. If voting is so very absolute and divine (which I am inclined rather to doubt myself), then certainly we have some of the authority that belongs to the founders of a true religion, the bringers of salvation." When the Hindu takes this very haughty tone and demands a vote on the spot as a sacred necessity of man, I can only express my feelings by supposing the situation reversed. It seems to me very much as if I were to go into Tibet and find the Grand Lama or some great spiritual authority, and were to demand to be treated as a Mahatma or something of that kind. The Grand Lama would very reasonably reply: "Our religion is either true or false; it is either worth having or not worth having. If you know better than we do, you do not want our religion. But if you do want our religion, please remember that it is our religion; we discovered it, we studied it, and we know whether a man is a Mahatma or not. If you want one of our peculiar privileges, you must accept our peculiar discipline and pass our peculiar standards, to get it."
Perhaps you think I am opposing Indian Nationalism. That is just where you make a mistake; I am letting my mind play round the subject. This is especially desirable when we are dealing with the deep conflict between two complete civilisations. Nor do I deny the existence of natural rights. The right of a people to express itself, to be itself in arts and action, seems to me a genuine right. If there is such a thing as India, it has a right to be Indian. But Herbert Spencer is not Indian; "Sociology" is not Indian; all this pedantic clatter about culture and science is not Indian. I often wish it were not English either. But this is our first abstract difficulty, that we cannot feel certain that the Indian Nationalist is national.
He immediately translated it into Gujarati, and on the basis of it he wrote his book Hind Swaraj, his own first formulation of a specifically “Indian “ solution to his country’s problems. Thus you might argue, not quite absurdly, that India owed its independence, or at least the manner in which it came, to an article thrown off by Chesterton in half-an-hour in a Fleet Street pub.
This account was first described in Gandhi by Geoffrey Ashe (Stein & Day, NY, 1968) p. 137-138, and is repeated in his new book, The Offbeat Radicals (London, Metheun, 2007).
I also have a fascinating interview with GKC that was published in the NY Times in 1916. It is with an Indian journalist, and Chesterton repeats his point that India should be for Indians. Use a library's article research function, and look up:
"India for Indians, Says Gilbert K. Chesterton", by Harendranath Maitra, New York Times, May 21, 1916 subtitled: Noted English Author Declares That She Must Be Nationalistic and be Represented as a Nation in Councils of British Empire. Indian author Maitra interviews GK Chesterton in this fascinating piece.
Here is something you can look up in the Chesterton Review.
Feb 1993 Vol XIX No 1 pp 88-93 of Chesterton Review which quotes some of Gandhi's actual writing about GKC.