gistfile1.txt

add_action( 'template_redirect', 'default_search_form_to_lettings' );
function default_search_form_to_lettings()
{
    global $post;
    
    if ($post->ID == 2) // REPLACE '2' WITH THE PAGE ID OF YOUR LETTINGS PAGE
    {
        $_GET['department'] = 'residential-lettings';
    }
}