The pound in particular is very old, and the practice of using a crossbar on the ascender of a letter to mark an abbreviation dates back to medieval times (http://en.wikipedia.org/wiki/Scribal_abbreviation#Suspension). In fact, given the proximity of the British pound's creation and the period during which these abbreviations were at their peak, it seems to me to be possible that the British pound was the first still-extant currency symbol that was a letter with a dash through it, nearly a thousand years earlier. I don't know if that would have formed a convention though.
The dollar is entirely different, and is essentially just a peso sign.
