Special Branch do not publish a centralised list of email addresses. Some forces public an email address on their own website, but this is hit and miss.
The way they want you to contact them is by fax. They publish a list of fax numbers on page 2 of the GAR form, but often these don't work! If you don't have access to a fax machine, then I suggest that you call them on the number published on the GAR and see if they can give you an email address or take your details over the phone. You need to give them 12 hours notice by law, but often they request 24 hours notice.
Customs will not acknowledge your email, or at least they never have for me.
Some special branch forces expect you to ring them up for a "confirmation number" but this is not law. How you are supposed to know which ones want you to I have no idea. I just keep a copy of the fax confirmation page and bring it with my on the flight. (Very useful recently on a flight to Oban when the SB claimed that I never faxed them. They calmed down very quickly when I showed them the fax confirmation page and suddendly what was a very serious problem was just a minor issue and no probem at all
)
The position within Ireland has changed a lot recently. The position with Customs seems to be that you don't have to notify customs of your flight but you do have to notify the airfield operator. The airfield operator may impose conditions on you before they will allow you to arrive/depart internationally from their airfield. The only two that I'm aware of at present is Weston which requires 24 hours notice to the Airfield, and Kilrush which require you to give 3 hours notice directly to Customs.
The immigration position in Ireland is a total mess, and I can't get a straight (official) answer from anyone in immigration. I've a friend who works in Immigration and asked him informally, and was told "Oh, we've (as in immigration) nothing to do with small aircraft!"
As best as I can tell, if your a UK or Irish citizen then you don't need to do anything for immigration. If your a non-UK/Irish citizen then you need to go through a port of entry, but that's only my very confused understanding
Suffice to say that because immigration don't seem to know what they are doing here, noone pays any attention to them
Don't sumuggle any refugees in, and comply with any requirements your airfield operator puts on you with regards to Customs, and you don't get into trouble on this side of the water
I hope that helps!
dp
ps. When you're leaving the Republic, tell the refuller that you're leaving the country and you'll get your fuel duty free