The page you are trying to scrape uses a poor HTML markup: many <a> tags are not closed. WWW::Mechanize gets confused and puts all the table into one link:

print $_->text, "\n" for $mech->find_all_links;
[download]

However, you can count the pages yourself and build the URL from pieces, not getting it from the page:

#!/usr/bin/perl
use warnings;
use strict;

use WWW::Mechanize;

my $search_url = 'http://careers.republic.co.uk/pb3/corporate/Republic
+/search.php';
my $mech = WWW::Mechanize->new();

$mech->agent_alias('Mac Safari');
$mech->get($search_url);

my $page_number = 1;
PAGE: while (1) {
    $mech->get("$search_url?page=$page_number");
    print " *** $page_number *** \n";
    print $_->text, "\n" for $mech->find_all_links;
    last PAGE if $mech->content !~ /Next/;
    $page_number++;

}
[download]

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