Removing Parent Page(s) from Permalink

Similar questions have been asked before, but no answer suits well.

I have: http://ift.tt/1Ika7EL and would like to have: site.com/child-page

So I want to exclusively have permalinks with depth 1, without using the custom menu but still "hierarchizing" my pages in the admin all pages view and with parent/order in page attributes.

The solution also needs to work automatically, so not changing permalinks on each page with the plugin "Custom Permalinks".

This is what I need, and I am sure it is possible with a few lines of code in the functions.php, which I have found elsewhere but only for posts to remove the category, but not working for pages to remove the parent.

This is such a code, that maybe can be changed to work for pages?

Thanks in advance, Sofian

add_filter( 'post_link', 'remove_parent_cats_from_link', 10, 3 );
function remove_parent_cats_from_link( $permalink, $post, $leavename )
{
$cats = get_the_category( $post->ID );
if ( $cats ) {
// Make sure we use the same start cat as the permalink generator
usort( $cats, '_usort_terms_by_ID' ); // order by ID
$category = $cats[0]->slug;
if ( $parent = $cats[0]->parent ) {
// If there are parent categories, collect them and replace them in the link
$parentcats = get_category_parents( $parent, false, '/', true );
// str_replace() is not the best solution if you can have duplicates:
// http://ift.tt/1CQFM1Z will be stripped down to myexamplesite.com/
// But if you don't expect that, it should work
$permalink = str_replace( $parentcats, '', $permalink );
}
}
return $permalink;
}