The case for seeing the Republic as primarily an ethical work, as in the ancient tradition, is developed in Chapter 4 of Julia Annas, Platonic Ethics Old and New (Ithaca, 1999).
There has been extensive work on the impact of ancient Greek culture on the Victorians, but there is little good on ancient philosophy. Of the available books, the best is Frank Turner, The Greek Heritage in Victorian Britain (New Haven, 1981); see also his article, ‘Why the Greeks and not the Romans in Victorian Britain?’ in G. W. Clarke (ed.), Rediscovering Hellenism: the Hellenic inheritance and the English imagination (Cambridge, 1989).
On the role of the Utilitarians see Kyriakos Demetriou, ‘The Development of Platonic Studies in Britain and the Role of the Utilitarians’, Utilitas 8 (1996). Two excellent articles are John Glucker, ‘Plato in England: the Nineteenth Century and After’, in H. Funke (ed.), Utopie und Tradition: Platons Lehre vom Staat in der Moderne (Würzburg, 1987) and ‘The Two Platos of Victorian Britain’ in K. Algra et al. (eds.), Polyhistor (Leiden, 1996).
I have considered England; for the early American tradition see Carl J. Richard, The Founders and the Classics (Cambridge MA, 1994). The European tradition differs between countries and is highly complex: see the papers in Ada Neschke-Hentschke (ed.), Images de Platon et Lectures de ses Oeuvres: les interprétations de Platon à travers les siècles (Louvain-Paris, 1997.
Grote’s Plato and John Stuart Mill’s long review of it are still richly rewarding; see Mill’s Collected Works, vol XI (Toronto, 1978).
The quotations from Popper are from The Open Society and its Enemies, vol 1 (London, 1945). John Wild’s book was published in Chicago in 1953. Whitehead’s very famous remark is from Process and Reality (Cambridge, 1929), Part 2, chapter 1, section 1. The History of the University of Oxford is edited by T. Aston, and the quotation is from p. 529 of vol. 5, The Eighteenth Century (Oxford, 1986).
Xenophon’s story comes from his Memorabilia (Reminiscences of Socrates), Book II, 1. Evidence for the sophists’ ideas can be found in R. McKirahan’s Philosophy before Socrates (Indianapolis, 1994). Ancient eudaimonist theories are set out and discussed in Julia Annas, The Morality of Happiness (Oxford, 1993). Aristotle’s major theoretical discussion of happiness is in Book 1 of the Nicomachean Ethics. The views of Epicurus and the Stoics on happiness are best studied in books 1–4 of Cicero’s On Moral Ends (De Finibus); see the English translation by Raphael Woolf (Cambridge, 2001).
On Socrates see Christopher Taylor’s Socrates (Oxford. 1998), an excellent short introduction. Socrates’ own account of the oracle is in the Apology. Socrates served as the symbolic figure of the ideal philosopher for most ancient schools; the Epicureans are the main exception; for them the ideal philosopher should be as serious and unironic as Epicurus. Plato’s most elaborate account of knowledge is in the central books of the Republic; his attacks on relativism, and indications of his concern with empirical knowledge, are in the Theaetetus. Aristotle’s discussion of the structure of a science is in the difficult Posterior Analytics; see also the opening chapters of Books 1 and 2 of the Metaphysics for his account of the development of knowledge, and Parts of Animals, Book 1, chapter 5, for a defence of studying widely differing kinds of subject-matter. An indispensable introduction to the wide range of ancient theories of knowledge is S. Everson (ed.), Epistemology (Cambridge, 1990).
For Aristotle’s logic see Robin Smith’s translation of the Prior Analytics (Indianapolis, 1989) and his chapter in the Cambridge Companion to Aristotle, ed. J. Barnes (Cambridge, 1995). There is unfortunately no good English translation of the sources for Stoic logic; see the relevant sections of Inwood and Gerson, and of Long and Sedley. The sources are collected in Karlheinz Hülser, Die Fragmente der Dialektiker der Stoiker, 4 vols (Stuttgart, 1987).
On Hellenistic science see G. Lloyd, Greek Science after Aristotle (London, 1973). For clear introductions to Aristotle’s metaphysics and philosophy of science see the chapters in the Cambridge Companion to Aristotle. There is little sustained philosophical discussion of Stoic and Epicurean metaphysics; there is, by contrast, a huge literature on Plato’s ‘theory of Forms’: see the Cambridge Companion to Plato.
The Further Reading gives suggestions for following up the history of ancient philosophy. The quotation from Martin West is from ‘Early Greek Philosophy’ in The Oxford History of Greece and the Hellenistic World, (Oxford, 1986). The comment that Plato is just Moses in Greek is fragment 8 of Numenius, a second-century Platonist who tended to see all Great Ideas in different cultures as being the same. Eusebius, in X 1 and XI 1 of his Preparation for the Gospel, claims more strongly that Greek philosophy steals all its ideas from the Jewish scriptures. The contrasting quotations about the nature of the beginnings of Greek philosophy are from John Burnet, Early Greek Philosophy (London, 1892) pp. v, 13, 28, and from Francis Cornford, Principium Sapientiae: a study of the origins of Greek philosophical thought (Cambridge, 1952) pp. 154–155.