I'd agree with what Don and Ray above have said, and that generic singing teaching can be useful for any singer. A good teacher will help you get control of your voice so that you can get it to do what you want. If you learn to sing in a very plain, unornamented way, you can then add any inflections or ornamentation you want, whereas if you start off with mannerisms copied from records etc (in any genre of music), you may find it difficult to drop them.
I'm not sure what a traditional "celtic" style would entail - really that term applies best to singing in the gaelic languages, which I don't imagine is what you're doing.
Irish singers, even singing in English, often use a lot of ornamentation, which you can learn from listening to performers and recordings, if that's what you're after. English and Scottish singing styles vary considerably, but there are certain common features that distinguish traditional from "classical" singing: Avoid the use of vibrato and keep a nice steady tone Keep the pitch in a comfortable range, rather than pushing the voice as high as possible Keep to the accent and pronunciation that you've chosen - the choice of accent is a whole nother issue that I won't deal with here, but try to avoid distorting the vowels too much or spitting out the consonants as choir-boys do. And above all, think all the time about the song and what it's conveying, rather than about the sound you're making. It's not about you, it's about the song. The words matter, the tune matters. That approach is what marks out the most of the good and respected traditional singers, and it's often somewhat lacking in both classically trained singing and bad folk singing.