Well, with the help of another post I've managed to solve the problem, everything works bar the media upload buttons (any suggestions?):
In your plugin you need to enqueue the following within the admin_print_scripts action:
wp_enqueue_script('post');
if ( user_can_richedit() )
wp_enqueue_script('editor');
add_thickbox();
wp_enqueue_script('media-upload');
wp_enqueue_script('word-count');
On the page writing your textarea to the page, replace it with the following:
<div id="poststuff">
<div id="postdivrich">
<h3><label for="content">Your Label</label></h3>
<?php the_editor($content, $id = 'content', $prev_id = 'title', $media_buttons = true, $tab_index = 2); ?>
</div>
</div>
The parameters for the_editor are:
$content - content to echo into the textarea
$id - id to give the textarea element
$prev_id - not sure what this is, I used an empty string
$media_buttons - set to false because they don't work in my implementation
$tab_index - not sure again, but default value works
I hope this is of some use :)
NOTE: If you do not specify 'content' as your textarea ID, it will not get initialised correctly!