Yup - I was going to suggest barley straw, but I see you have already.
If I were doing it and had room, I'd consider passing the water through
a small reedbed, then the straw, and into a sand filter.

Seriously, whatever the quality of the water which went in, you could
safely drink the water which came out.

If anyone is interested, I'll make a set of instructions and a diagram
and put the result up as an HTML page on the wibble.

I would take you up on this, if no one else will
I have thought vaguely about setting up a reed bed, but I am not
even sure which type of reed to use.

Dave H