For the general case of breaking any long line into a bunch of lines having some maximum width, you want Text::Wrap. Others have stated better ideas for your specific case, but you could also do it like this:

$Text::Wrap::$columns = 50;
$new_string = Text::Wrap::wrap( '', '<br /><br />', $string );
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You'll notice that the wrap function will always include a "\n" as part of the line break (it appends "\n" at the end of each output chunk), and the width of the "indent" args (the <br /><br /> for non-initial lines, in this case) will be counted as part of the final line-width. I haven't studied the entire man page myself yet, and there's probably lots of flexibility...

But if you're really picky and you believe that Text::Wrap won't do exactly what you want, then something like the following would be simpler than the code you posted:

my $new_string;
my $width = 50;
while ( length( $string ) > $width ) {
    my $brksp = rindex( $string, ' ', $width );
    $new_string .= substr( $string, 0, $brksp ) . '<br /><br />';
    $string = substr( $string, $brksp+1 );
}
$new_string .= $string;
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(update: replaced literal "50" with $width in "while" condition)