Obviously, the most influential English writer during the age of Chaucer (basically, the second half of the fourteenth century) was Chaucer himself. He published the immortal (but incomplete) The Canterbury Tales in 1400, the year of his death, and the collection of stories became widely admired and very influential.
Other influential English writers of the period include William Langland, who is credited with writing Piers Plowman sometime around the 1370s, and John Mandeville, whose quasi-fantasy account entitled The Travels of John Mandeville depicted the author's journeys through the Middle East and beyond. The "Pearl Poet," the unknown author of a poem by that title as well as, probably, the poem Sir Gawain and the Green Knight, is also a well-known writer from the period.
Other writers who were influential among learned circles in England included the Italian writer Giovanni Bocaccio, whose Decameron influenced The Canterbury Tales; and Petrarch, whose writings are actually mentioned by Chaucer.