No one can be pointed out as the person(s) that put the English alphabets in order. Alphabets were introduced first by Phoenicians. The Phoenician alphabets had 16 characters. In the 8th century BC, the Greeks adopted the Phoenician alphabets, the Greeks introduced vowels to the alphabets as all the alphabets in the Phoenician alphabets were consonants.
The Romans took this new set of alphabets from the Greeks and organized it into the modern alphabets we have today. Many scholars believe that the alphabetical order was based on the order of Egyptian hieroglyphics.
The reason that the English alphabet is put in the order that it is is that it inspired by some of the other great alphabets that came before it. These alphabets are namely the Greek Alphabet and the Phonecian Alphabet. The major influences on the reason that the English alphabet is in the order that it is are Early Phoenician, Greek, and Proto-Sinaitic. Proto-Sinaitic is a writing form that is known as Pre-Caananite and was very influentual in formation of Hebrew and the early languages that are seen in the Holy Bible.
It was during the early part of this period that it was decided that only a certain amount of symbols would be used to form a standard alphabet. All kinds of symblols were used during the time just like it was with heiroglyphics and the writing system of the acient Egyptians. The order of the English alphabet was designed to mimic that of the more established alphabets before it, namely the Phonecian and Greek alphabets. The English alphabet is certainly one of the most ifluentual instruments in the history of the planet Earth.