There is no such thing as an "English" accent. Instead there are dozens of British accents. Generally these are regional or class based. Famously this was shown off in the play Pygmalion, later worked into the musical My Fair Lady. In that the fictional Henry Higgins teaches a Cockney (Lower class accent from a part of London) iflower seller to speak in a Received Pronunciation accent and enters her into high society.

When the US was settled it was settled by folks from across the British Isles and later from across Europe and the world. This melange of languages and accents blended uniquely in various US regions to create new accents and dialects. The Appalachian (hillbilly) accent/dialect for example draws primarily from their Scotts-Irish ancestors. It is inevitable that speakers in a place like Louisiana which is heavily influenced by French, African, and Caribbean languages, would end up different from say Boston which has few of those influences.

Finally I should point out that accents do change over time. Even if the US had been settled entirely by speakers of a single accent, it would today differ from the modern speakers of that accent in the UK. No one speaks with a Shakespearean accent today anymore.