What did "18/9", "25/", and "30/" mean in this 1800 British document?
Yes your guess is correct.

In fact, the forward slash punctuation mark "/" actually comes to us through its being the abbreviation for the English shilling.

From Humez and Humez (2008):


  ... forward slash (/), which is also variously known as a solidus, virgule, or just plain slash, when the deletion of a single character is to be marked. The solidus was a Roman coin and is ultimately the basis for English soldier, the idea being that a soldier is someone who fights for money, or, as we might say today, a mercenary (from the Latin merces ‘wages.’) The solidus as slash is historically a straightened-out S, the abbreviation for the English shilling (as in 2/3—two shillings thruppence), the step from one coin to another being relatively easy. How we get from shilling to slash in its various other uses—as proofreader’s strike-out mark, arithmetical sign of division, general separatrix, and so on—is rather more murky.