Who among the following called John Dryden as the father of English Criticism and affirmed that modern English prose began with Dryden’s Essay of Dramatic Poesy?

The correct option is Samuel Johnson.

To understand why this is the correct answer, let's look at the historical literary context of these remarks:
Dr. Samuel Johnson, the eminent 18th-century English writer, critic, and lexicographer, famously praised John Dryden's contributions to English literature and criticism. In his work Lives of the Most Eminent English Poets (specifically in the biography of John Dryden), Johnson wrote:
"Dryden may be properly considered as the father of English criticism, as the writer who first taught us to determine upon principles the merit of composition."

Furthermore, Samuel Johnson also credited Dryden with shaping the course of modern English prose style, pointing specifically to works like the Essay of Dramatic Poesy (1668) as the starting point where English prose took on a modern, refined, and elegant form, escaping the convoluted structures of earlier Elizabethan and Jacobean writers.

Therefore, Samuel Johnson is the figure who made these influential assertions about John Dryden's legacy.