I might suggest getting a car in London, drive to the west coast, probably take a ferry from Wales, then do the big loop, going south from Dublin (Or wherever the ferry of choice lands)first. By the way, if you choose the ferry, reservations are almost esential.
Lil Seaside lived in London for several years and we made several trips over there, did the north part of England, Scotland and all that, but Ireland is far and away the better place to visit IMHO. People are friendly, lots to see. We always took pot luck on bed and breakfast and came out famously. Get a Frommers and make some definte stop plans ahead so you don't get slammed on time.