Although the origins of the Ogham alphabet are disputed, it is clear that the graphically innovative system has its roots in already existing alphabets, probably the runes and/or the Etruscan and Latin alphabet. Many writing systems have letters with new forms, but this does not mean that the idea of writing alphabetically has been re-invented in those cases. Han-kul for example has – on a formal level – little in common with alphabetic scripts in use in the vicinity of Korea, however, the creator(s) of the alphabet were certainly aware of Indic alphabets such as the Mongolian 'Phags pa (DB 225). The script may be formally closer to Chinese, but its structure is clearly alphabetic, and the fact that each consonant is accompanied by a vowel letter below has a close parallel in Indic scripts where consonant and vowel letters merge into quasi-units.
The similarities between Ogham and runes are in any case remarkable. Both systems are based on phonological and phonetic knowledge: in the case of Ogham, the vowels are in one row, dental /d, t/ and velar /k, k_w/ stops are all placed next to each other as well as fricatives /f, s/ and velar sounds /g, N/. It is also interesting to note that all Ogham letters, including the odd [st]-symbol (sometimes transcribed as <z>, DB 341), have Anglo Saxon runic counterparts. Of course, it is necessary to examine whether these letters are due to phonetics and/or phonology or rather to the model given by another alphabet (runic or Latin). Also, it is not clear how this symbol was actually pronounced.
At the same time, the creativity of the creators of Ogham as well as other alphabets should not be underestimated: the vowel order is probably based on the distinction front/back: back vowels /a, o, u/ [A, o, u] are followed by front vowels /e, i/. The shape of the letters is certainly also rather original, as in the case of the Korean Han-kul or in the case of some runic characters.
Crystal (205) states that Ogham letters symbolized either Gaelic or Pictish phonemes. The alphabet was probably created around the 4th century BC. It can be found on rocks, stones and pottery in Wales and Ireland. According to Babaev, Old Irish ogam is not a Celtic word. Although Pictish is probably a non-Indo-European language, Celtophiles argue that due to the fact that there is no /p/ letter in Ogham Pictish itself must be a Celtic language. Babaev assumes that there was probably some Celtic influence on Pictish.
Daniels, Peter T. and William Bright. 1996. The world's writing systems. NY and Oxford: OUP 1996. (=DB)