Yes, there is a law governing wrecks. They are not just there for anyone to steal from. This is called the Law of Salvage. There are three main sections which cover salvage.
In simple terms, the protection of Wrecks and the protection of Military remains acts detail what salvors can't do, and the Merchant Shipping Act covers what salvors can or must do.
Under U.K law, all vessels are presumed to have an owner whether it be an individual, an insurance company or underwriters. Therefore the first thing that anyone must do before salvaging anything is to make every effort to trace the owner with a view to obtain permission. If a wreck was recovered within U.K territorial water and no owner establishes a claim to the property within one year of it being reported to the Receiver of Wrecks, then it generally becomes the property of the Crown. If the vessel was recovered out with the U.K limits then the crown makes no claim. So, if at the end of the one year period to claim has been made then the property is returned to the salvor.
The photo was reproduced by the kind permission of John Liddiard