So how then, were the Fabians influenced by Utilitarianism? Judging from what I'm reading in Edward Pease's "The History of the Fabian Society", Utilitarianism is probably not the largest influence. But it can't be ignored either. Here are some general observations:
First, as I wrote earlier, Henry George was an important ideological driver for the Fabians. But as Pease's writing makes clear, George was not the only one. Chapter 1 of Pease's 'History' is titled "The Sources of Fabian Socialism" to which:
The ideas of the early eighties—The epoch of Evolution—Sources of Fabian ideas—Positivism—Henry George—John Stuart Mill—Robert Owen—Karl Marx—The Democratic Federation—"The Christian Socialist"—Thomas Davidson
To those of you not well versed in all of these things(and I don't consider myself an expert either, I'm just observing) John Stuart Mill is the Utilitarian key here. I also bolded Positivism, because that's Auguste Comte's ideals. I've not seen that in my classes, but it's something that Mill himself had wrote about, and not in a way that I would consider favorable to liberty.
But keeping with Utilitarianism and Fabianism, here is one of the first things written about Mill in Pease's 'history':
(quoting Mill)"We are too ignorant, either of what individual agency in its best form or Socialism in its best form can accomplish, to be qualified to decide which of the two will be the ultimate form of human society."
More than thirty years had passed since this had been written, and whilst the evils of private property, so vividly depicted by Mill, showed no signs of mitigation, the remedies he anticipated had made no substantial progress. The co-operation of the Rochdale Pioneers had proved a magnificent success, but its sphere of operations was now clearly seen to be confined within narrow limits. Profit-sharing then as now was a sickly plant barely kept alive by the laborious efforts of benevolent professors. Mill's indictment of the capitalist system, in regard to its effects on social life, was so powerful, his treatment of the primitive socialism and communism of his day so sympathetic, that it is surprising how little it prepared the way for the reception of the new ideas. But to some of his readers, at any rate, it suggested that there was an alternative to the capitalistic system, and that Socialism or Communism was worthy of examination.
I could go on quoting Pease at length, but I'm hoping people will click the link and do so for themselves. The above is certainly written favorably to Mill. Other parts of the book are certainly favorable as well, though at several times(as I mentioned at the beginning) the question arises as to just how influential Mill really was. My goal here is not to lay it all at the feet of Utilitarianism, as the facts simply do not warrant that. My goal is to get people thinking that perhaps there's more than one way for professors to get their students to start thinking that big government is the only correct course of action for society. It doesn't have to be communist or socialist propaganda.
Of the things I've found relating to Utilitarianism and Fabianism, four stand out and are worth the read to those interested:
1: "Shaw, the Fabians, and the Utilitarians" by William Irvine Lays out many things pretty well, including those things which are unwritten. For example, Beatrice Webb's parents, and their role in earlier Utilitarianism.
2: The Rise and Fall of England: 11. The Fabian Thrust to Socialism, an article on The Freeman which also details the influence of the Utilitarians.
3: The third is a writing by G. D. H. Cole, titled "Fabianism". Cole was himself a member of the Fabian Society, so he is yet another solid source for this, and to which unlike other writings seems to explain why the Fabians rejected many parts of Mill: (Page 3)
John Stuart Mill they recognized as standing at the point of transition between the two interpretations of utilitarianism. Although he sympathized with the socialism of his day, he was too deeply rooted in the old traditions for a complete conversion. The Fabians regarded themselves as completing the work which he had begun and thus found further cause to emphasize their continuity with older liberal thought.
4: Another member of the Fabian Society, Bertrand Russell, wrote the following, to which is displayed prominently upon one of the home pages of today's utilitarians, utilitarian.net(this comes from Page 39 of his autobiography)
It appeared to me obvious that the happiness of mankind should be the aim of all action, and I discovered to my surprise that there were those who thought otherwise. Belief in happiness, I found, was called Utilitarianism, and was merely one among a number of ethical theories. I adhered to it after this discovery.
I'm satisfied that the answer to the original question is an affirmative - Utilitarianism leads to Fabianism.