Ok, I've done some more reading - let me see if I've got this right:

LWP::Simple returns HTML which is encoded in ISO-8859-1 (Latin-1).
XML::Parser defaults to UTF-8 (unicode) if the XML does not specify an encoding.

So using:
my $rss = new XML::RSS( 'encoding' => 'ISO-8859-1' );

should work.

It doesn't.