I have managed to solve this problem by creating my own code.
In my content-excerpt.php
template part, I have included the following,
if(!is_page('Home')){
$page = get_page(get_the_ID());
$custom = get_post_custom($page->ID);
// I have added a custom field on the page, which contains the category id
$custom_post = get_posts(array('numberposts'=>1, 'category'=>$custom['Category Link'][0], 'post_type'=>'post', 'post_status'=>'publish'));
$post = $custom_post[0];
}
Which I can then use in the normal way, with things like the_title()
Hope someone finds this handy.