No single person did, the modern-day English Alphabet is not a conscious creation of a single genius mind, but has a long history in itself.

This is the modern-day English Alphabet.

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Before the Renaissance the vowels I and U could be used as semi-vowels (I = J) or consonants (U = V), this was not depicted in the script, rather I/J and V/U were variations of the same character which marked no differantiation in pronounciation whatsoever. To make the phonemes clearer the differentiation between I/J and V/U was introduced back then. The character W is a double letter, out of two Vs (hence its english name "double u"), which was likewise introduced after the Middle Ages.

So before the Renaissance we have.

A B C D E F G H I K L M N O P Q R S T V X Y Z

The two letters Y and Z were added to the Latin Alphabet after the Roman conquest of Greece when an influx of Greek loanwords demanded the depiction of phonemes not present in the Latin Alphabet - Ypsilon (Y) and Zeta (Z).

A B C D E F G H I K L M N O P Q R S T V X

The G was introduced to depict the phoneme /g/ in contrast to C /k/ in earlier Roman times; it replaced the Old Italic Z which had no use in Latin language.

A B C D E F Z H I K L M N O P Q R S T V X

These are the 21 characters of the Archaic Latin Alphabet. Those did derive from the Western Greek Alphabet, among other Italic Alphabets (like the Etruscian, for example). The Western Greek Alphabet differs quite a lot from the Eastern/Ionian Alphabet which became the precursor to the classical Greek Alphabet; it was spread to Italy most likely through the Greek colonies in Southern Italy. Both scripts derive from the Phoenician Alphabet, but the Western Greek Alphabet kept some phonemes from the Phoenician which were dropped in the classical Greek Alphabet (notably /q/ and /h/ and the Digamma (/w/) which developed into our /f/; Χ as /ks/ instead of classical Greek /kh/).

Α Β Γ Δ Ε Ϝ (Digamma, /w/) Ζ Η (not Eta, but Heta, /h/) Θ Ι Κ Λ Μ Ν Ο Π Ϻ (San, /s/) Ϙ (Koppa, /q/) Ρ Σ Τ Υ Χ (spoken as /ks/ similiar to classical Greek Ξ) Φ Ψ (spoken as /kh/ similiar to classical Greek Χ)

Compare:

Α Β Γ Δ Ε Ϝ Ζ Η Θ Ι Κ Λ Μ Ν Ο Π Ϻ Ϙ Ρ Σ Τ Υ Χ Φ Ψ

A B C D E F Z H (-) I K L M N O P (-) Q R S T V X (-) (-)

One can easily spot the smiliarities between the Archaic Latin and the Western Greek Alphabet here - the Latin one did drop the diphthongs (Θ /th/, Φ /ph/, Ψ /kh/) and didn't seperate the two characters for /s/ (Ϻ, Σ).

As said before the Western Greek Alphabet goes back to the Phoenician Alphabet, which only consisted of consonants, because vowels in the semitic languages play a different role than in indo-european ones - it's not as necessary to depict vowels for the understanding of words as most words go back to certain consonantical roots.

Α Β Γ Δ Ε Ϝ Ζ Η Θ Ι Κ Λ Μ Ν (-) Ο Π Ϻ Ϙ Ρ Σ Τ Υ Χ Φ Ψ

𐤀 𐤁 𐤂 𐤃 𐤄 𐤅 𐤆 𐤇 𐤈 𐤉 𐤊 𐤋 𐤌 𐤍 𐤎 𐤏 𐤐 𐤑 𐤒 𐤓 𐤔 𐤕 (𐤅) (-) (-) (-)

Phoenician characters used by the Greeks to depict vowels (Α, Ε, Ι, Ο, Υ) were those who had no phonetical use in Greek language (like 𐤀, Alep, being a glottal stop (ʔ, like in "be-hind")) or those who are semi-vowels anyway (𐤅, Waw, as /w/; 𐤉, Yod, as /j/). The diphthongs are special greek phonemes with no parallel in the Phoenician Alphabet, but the shape of their characters is obviously taken from the Phoenician one, too.

The Phoenician Alphabet itself may stem from older semitic alphabetical writing systems, like the Proto-Sinaite-Script (which may have been derived from Egyptian Hieroglyphs). A parallel phenomenon is the Ugaritic Alphabet, which formed an Alphabet out of the Cuneiform, possibly under the influence of Proto-Phoenician-Alphabets. Ugaritic clay tablets already show lists with an Alphabet in (roughly) the same order as its later successors and appear to be the earliest Abecedaria (written order of an Alphabet).

𐤀 𐤁 𐤂 (-) 𐤃 𐤄 𐤅 𐤆 𐤇 𐤈 𐤉 𐤊 (-) 𐤋 𐤌 (-) 𐤍 (-) 𐤎 𐤏 𐤐 𐤑 𐤒 𐤓 (-) (-) (𐤔) 𐤕 (-) (-) (-) [Phoenician Script]

ʔ b g (-) d h w z h tˤ j k (-) l m (-) n (-) s ʕ p s q r (-) (-) (sh) t (-) (-) (-) [Phoenician phonemes]

ʔa b g (kh) d h w z h tˤ j k (sh) l m (d) n (z) s ʕ p s q r (t) (g) (-) t (ʔi) (ʔu) (s) [Ugaritic phonemes]

We call this order the Abgad, after its initial phonemes (ʔ(a)-b-g-d), which is the basis for most semitic and indo-european Alphabets today. Why this order? We do not know. As an Alphabet it is designed to be memorised, this order may have phonetical reasons - so that it's easier to speak, easier to memorise (like the "ABC"-song). But as far as I know there has not yet been an answer to this question, that would have been widely accepted.

It is worth noticing that the Abgad isn't the only order we find on Ugaritic clay tablets - the Halahama (h-l-ḥ-m) is another order that roughly correspondents with ancient South Arabic and Ge'ez' Alphabets.

Edit: Tried better formatting with the Alphabets, but reddit is a bitch. Sorry, it may be a bit confusing to look at.