I've got good news and bad news. The bad news is that I'm American and lived in Ireland for five years and I still can't do a convincing Irish (or British--whatever that is) accent.
The good news is that your writing makes a good impression so if that's accurate I imagine you'll be able to communicate just fine. People just have accents, they're not seen as negatively in English as learners seem to think. In fact, there will always be somebody who thinks a certain accent is sexy so there are benefits too!
The only accents I can do is when I am copying someone, so you can try my method... it's free! Take a video or audio recording of an accent you like/admire, preferably with a transcript, listen to it and record yourself copying it. Listen to yourself and the original again and self-correct until you get it right. You can use websites or ask more questions here if you need help with the technical aspects.
You can get videos here:
euronews.net: all of the Top Stories have videos with transcripts
BBC Learning English: all of the Words in the News stories have recordings of the article (the pace of the speech is a little slow)
TED.com: a wide variety of speakers, but it's natural language at a natural presentation pace and the community will transcribe and translate all of the talks
Don't worry so much about the individual consonant and vowel sounds (as long as they are distinct and comprehensible), try to notice sentence stress patterns and intonations and you'll soon be more comfortable with your own unique accent. Check out Amy Walker if you haven't already.
Student or Learner