The first thing to note is that this study was done in the 50s and lots more broadside copies are now available, so Laws is far from being comprehensive. He didn't much bother with American printed examples as the title suggests, although many of the ballads were also printed in America albeit at a later date than in Britain. Laws would have had access to the Stationers registers and would have been aware that some of them were first printed in the 16th century although these would have appeared in Child and he seems to have avoided those ballads already with a designated Child number many of which appeared on broadsides on both sides of the Atlantic. Some of the ballads were still being printed into the 20th century but I can't remember seeing references to these in Laws. He didn't actually give printers' dates for any of his references so we can't be certain how recent the printings are. He must have had access to some of the larger collections and many of these go upto the 1880s or so. Also he was in some cases at least looking at style and conjecturing from content and style that they were from British broadsides without actually having seen the broadside. I should also imagine he was using references to broadsides from earlier anthologies from both sides of the Atlantic. To answer your question precisely you would have to go through the whole book and even then some of the references are vague.

If it's any help a rough guide is that the majority date from the late 18th/early 19th centuries. About 20% from an earlier period.