Ah, I’ve sorted it!
I only needed to add the posts page ID to the first call, like this:
<?php $post_object = get_field('prospectus', 674);
if( $post_object ):
// override $post
$post = $post_object;
setup_postdata( $post );
?>
<div class="side-box side-prospectus">
<img src="<?php the_field('image'); ?>" alt="<?php the_title(); ?>">
<h3><?php the_title(); ?></h3>
<p><?php the_field('description'); ?></p>
<?php
$file = get_field('pdf_file');
if( $file ): ?>
<a href="<?php echo $file['url']; ?>" target="blank" class="button small button-icon-right button-icon-download"><?php _e('Download (PDF)','anglocontinental') ?></a>
<?php endif; ?>
</div>
<?php wp_reset_postdata(); ?>
<?php endif; ?>
