Or, if you only have core modules at your disposal, then you could work out the first of next month and subtract a day:

use strict;
use Time::Local;

use constant ONE_DAY => 24 * 60 * 60;

my ($sec,$min,$hour,$mday,$mon,$year) = localtime();
$mday = 1;
$mon = ($mon + 1) % 12;
$year += 1 if($mon == 0);

my $time = timelocal($sec,$min,$hour,$mday,$mon,$year) - ONE_DAY;

print scalar localtime($time);
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Update: Sorry, I completely misread the question and gave you the last day of this month. The last day of last month is a little easier:

use Time::Local;

use constant ONE_DAY => 24 * 60 * 60;

my ($sec,$min,$hour,$mday,$mon,$year) = gmtime();
$mday = 1;

my $time = timegm($sec,$min,$hour,$mday,$mon,$year) - ONE_DAY;

print "Date: " . localtime($time) . "\n";

$mday = (localtime($time))[3];

print "Day of month: $mday\n";
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Update 2: As MarkM notes below, daylight savings changes could trip these snippets up. I originally coded them to set $sec, $min and $hour all to zero and then subtract say 4 hours - which I think should be pretty safe. I changed it before posting because I thought it was a bit obfuscated - but clear code that's wrong is no less wrong :-)