The influence of the Italian Renaissance on 15th-century English literature is extensive and far-reaching. I'll cite two specific examples of its influence for you.
First, English writers were influenced by the Italian sonnet form of poetry. They imitated Petrarch's sonnet form and created sonnets using the Italian form themselves. Then, English writers built on the form to create Spenserian sonnets and Shakespearean sonnets.
Second, the Italian Renaissance involved a rediscovery of Ancient Greek and Roman tragic drama. Thanks to the influence of the Renaissance dramatists and thinkers, Shakespeare and other writers also knew of and studied classical tragedy, and then wrote tragedies themselves. In short, without the Italian Renaissance, Shakespeare never writes Hamlet, Macbeth, Romeo and Juliet, etc., in the form that he does.