query_posts and only show results if a custom field is not empty

Try this code:

$args = array(
'posts_per_page' => '10',
'post_type' => 'programmes',
'meta_key' => 'popularityfig',
'meta_value' => '',
'meta_compare' => '!=',
'order' => 'DESC'
);

There’re 2 arguments you might want to note in the code: meta_value and meta_compare. Using meta_compare with operator != will exclude posts with empty meta value.