Want to move my sink from island to side worktop - will this be possible...

[another20]

...and costly?

Side worktop wall backs onto utility room from which I suppose we could run a waste pipe to an outside drain....or would we need to dig up the floor?

Depends where the supply comes in. The pipes to the island could possibly be disconnected and left under the floor. A new connection could then be made to the new location. Impossible to say without knowing the set up. If you have a cellar, it might be possible to put new feeds in from under the floor.