What were the influences of the Renaissance on English literature?
The Renaissance had a lasting impact in shaping English literature through the works of poets and dramatists like Ben Jonson, Christopher Marlowe, and most importantly, William Shakespeare.
For centuries since, the English Renaissance has had a lasting impact in shaping the traditions of English literature and drama. We can see this in Shakespeare's influence over the English language (he likely invented hundreds of words that are in common use today) as well as on the stage (consider how often his works have been interpreted and reinterpreted, with different generations finding something new to glean from his work).
One can also point to Renaissance expectations concerning poetry, the legacy of which would continue to shape the form for centuries afterward. Poets of the eighteenth and nineteenth centuries continued to use the same metrical structures that Elizabethan poets had used before them. Later, in the twentieth century, Modernists would break with those expectations through techniques such as free verse. Yet, even in their case, these poets were still interacting with Renaissance artistic norms by way of rebellion.
From this perspective, the Renaissance has had long-standing influence in shaping centuries of English literature. The works of Shakespeare and the metrical form continue to be relevant today.
On the other hand, if you wish to explore how Renaissance ideas were reflected within English Renaissance literature, that's a very different question. Most importantly, a humanist focus on Classical Antiquity is one of the defining features of the Renaissance period. In the English context, we see Classical references embedded throughout English literature. These references occur in Shakespeare's works, including Julius Caesar and Antony and Cleopatra (and even A Midsummer Night's Dream, with its inclusion of Theseus and Hippolyta).
In addition, we can point to Shakespeare's poetry, with works such as Venus and Adonis and The Rape of Lucrece that were also derived from Classical Antiquity. We can also point to Christopher Marlowe's translations of Ovid and Lucan. These examples should give you a sense of the degree to which the humanist fascination with Antiquity was present in English literature during the Renaissance era.