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I'm guessing here, but isn't it about the 3 mile territorial waters rule? If the ship remains within 3 mile of the coast then the rules of that country apply. Maybe someone with a nautical background can comment.
The 3 miles is actually 12 so for most or all of its travels around the UK the ship will be within UK territorial waters so no casino when this is happening not sure even if the duty free shops on board the ship can open.
Territorial waters, or a territorial sea, as defined by the 1982 United Nations Convention on the Law of the Sea, is a belt of coastal waters extending at most twelve nautical miles from the baseline (usually the mean low-water mark) of a coastal state.
The question is a little confused, if not only by the fact that I think you are actually on the cruise at the moment, aren't you? The answer to you question is quite simple. After leaving South Queensferry, the ship spends a day at sea before reaching Le Havre in France. This obviously gives the ship the opportunity to leave British territorial waters and the "local regulations"! Happy cruising.