The growth of the novel was impelled by the technology of print, decreasing prices of paper relative to wages, and a dramatic increase in vernacular literacy.
The very earliest English novels, such as Lyly's Euphues were strongly influenced by the Greek novels of the second sophistic, primarily as mediated through the French of Amyot. They were pastoral in setting and had much of the ornate language and episodic character of their rhetorical heritage, and lacked strong plotting and characterization. The next major phase in the development of the novel was also influenced by a rhetorical genre, namely the letter-writing manual. Many English Renaissance epistolary manuals, such as A Post with a Packet of Mad Letters and The Enemy of Idleness organized model letters in such a way as to achieve a nascent plot structure; Richardson and Defoe, both of whom composed letter-writing manuals before moving into novels, developed fully plotted and characterized novels in letters. Many of the 18th century novels were in the genre of the picaresque, following the escapades of a single colorful character (Tom Jones, e.g.). Next came the Gothic novel, a popular form with strong plotting, suspense, and exotic locales, followed in the Victorian era, by a wide range of works, some focused on character (Trollope, Austen, etc.) and others on plot (the sensation novel). Changes in the novel over the 19th century were influenced by mass literacy and cheap (acid) paper, lead to the gradual separation of the literary from the popular novel form, a bifurcation that is most apparent in the contrast between the modernist or experimental novel and the pulp, genre, and mass market fiction of the 20th century.
As I am sure you can appreciate, this is a question that attracts much debate and criticism, with much fevered disagreement between the various academics that have tried to answer it. However, I will try and stick to the mainstream approach in responding to this question.
It is generally accepted that the modern novel was developed fully in the 18th century, and a number of the texts in English literature that jostle for the title of the first novel in English come from this time period. The one that most critics agree is the first modern novel is Robinson Crusoe by Daniel Defoe. However, in this period, a number of different kinds of novel were developed, such as the gothic novel, the sentimental novel, the historical novel, the epistolary novel and the libertine novel. Other texts that claim the title of the first novel are Don Quixote, Pamela and Pride and Prejudice.
In terms of the development of the novel as a distinct literary form, it is important to note that early epic classics such as Beowulf and the Aeneid are generally recognised as serving as literary stepping stones or transition points as the novel develops as a distinct literary form. Certainly it is after the 18th century that the novel begins to be a commonplace form of literature, with the Victorian years in particular allowing for its establishment and consolidation as many writers begin to use this form to publish their ideas and beliefs. Notable novelists from this period are of course Austen, Dickens, Thackeray, Trollope and Eliot to name but a few. It is interesting to reflect that the novel, which we so strongly associate with literature today, is actually only a relatively modern invention in terms of the history of literature.