Yeh, you want a 240 - 110v step down at 2A or bigger depending on how deep your pockets are.

The new one will be slightly different, but basically, the 240v goes in one side and the 110V out the other.
 Earth attaches to the chassis as you have in the pic... doesnt matter what way round brown and blue go ( active and neutral).

The really good thing about having a 3 core flex lead to the game is that you can ensure good earth to all metal parts by running a further earth wire to things like the door etc