I understand it as weight. A one-pound fish, or one pound of fish (meat). To mean a money amount, you'd say "one pound's worth of fish". Well, that's the standard English - you did notice the singer is not a native speaker, didn't you? Plus he has a sign behind him, so it's clear he means one fish for a pound sterling.

A pound of fish. Use lb. That is the measure of weight. The other £ is the monetary unit in England. We do not use it in the USA, but we do use lb. which is an abbreviation from a Latin word, which I think is Libre (or Libra), which means pound as a unit of weight measure. The tricky thing is that they both sound the same when you hear them spoken.