I've driven on the opposite side in Ireland and Australia. My biggest challenge is still roundabouts, as we don't have those in the U.S. I still can't tell who has the right of way in those, and more than once have circled around a second time to get out of one (have you ever seen the Vacation movie with Chevy Chase, where they continuously circle a roundabout in Rome because they can't get out?).

My first experience was in Dublin, leaving from the airport, which is on the outside of the City. Most of it was two lane country road, until you got to a stretch of motorway. I felt comfortable from the start, as I was not contending with a lot of traffic.

Have you considered flying into a smaller airport, or training out to somewhere where the traffic might be more managable? I would not want London Heathrow to be my first experience, knowing the traffic in and out of there.