Cheers for the rapid replies, guys.

I've tried the Levels adjustment trick, and possibly because there's
no actual white on the pic, i can't get white without washing out the
fainter black dotted lines. However, you have both suggested that
maybe i'm approaching this from the wrong end, and should be scanning
differently in the first place. I have a bog-standard HP 1350 3-in-1,
and I've been using the equally standard Windows scanner software.
There is no 'scan as line art' option that I can find. However, with
some messing about, using the HP scanner software, I've managed
slightly better results, but it always seems to be a fine balance
between losing the faint '- - - - -' type of lines, and turning the
grey white.