Filter query based on date in custom field

I have a custom post type jobs and custom field with key expiry-date which the user enters the date after which the post will no longer be displayed.

Here's my code so far...

$loop = new WP_Query( array(
            'post_type' => 'jobs',
            'posts_per_page' => -1,
            'order' => 'ASC',
            'orderby' => 'date',
            'meta_query' => array (
                'key' => 'expiry-date',
                'value' => date('d/m/Y',strtotime("today")),
                'type' => 'DATE',
                'compare' => '>='
            )
        ));

if (have_posts()) : while ($loop->have_posts()) : $loop->the_post();
    [display content]
endwhile; else:
    [display "no vacancies" message]
endif;

The date in expiry-date is stored in the format dd/mm/yyyy (although some posts may have this field empty). I'd like to only return posts in the query where the expiry date is greater than today's date (or doesn't have a date set) - I've tried various values and compare types what am I missing?