Don't worry - I worked it out
For future reference, this should work fine:
<ul>
<?php
$lastposts = get_posts('numberposts=10');
foreach($lastposts as $post) :
setup_postdata($post);
?>
<li><a href="<?php the_permalink(); ?>" id="post-<?php the_ID(); ?>"><?php the_title(); ?></a></li>
<?php endforeach; ?>
</ul>