If an island unit can be moved, that is it's not fixed to the floor, is it a table...?
We are constructing just such a unit for our kitchen- a 19C French "doughbox", as used to make bread. The oak carcase is original, but the 'counter-top' or 'lid' for kneading is long gone. We thought of putting new 2.5" thick Alder 'lids' on as I have some huge 20 year old air dried boards, as a pair of sliding countertops on ball-bearing runners, to use the space in the box. It won't be nailed down, as the floor is ceramic tiled and it weights a ton anyway.
