I replaced my Puck tap 2 years ago which is just like your brown folding one, its not a big job and very straight forward, its just a bit fiddly as there is not a lot of room, I didn't need to take the sink out...
. The one thing I do remember is cutting my hand on a sharp piece of metal from underneath tap hole in the steel sink where the plastic nut holds the tap.
Eriba Models do vary, just see if you can get your hand around the back to undo the nut holding the tap, once its loose hopefully you can pull it out with enough slack from the water pipe and wires.