You should be able to make an ajax call to the php script with an array of list_position=>item_id and then in PHP loop through said array with
update table set list_position='$key' where id='$val';
and then of course you would sort by list_position when selecting data on future queries.
Edit: Just found this example online @ http://wil-linssen.com/entry/extending-the-jquery-sortable-with-ajax-mysql/
JS:
<script type="text/javascript">
// When the document is ready set up our sortable with it's inherant function(s)
$(document).ready(function() {
$("#test-list").sortable({
handle : '.handle',
update : function () {
var order = $('#test-list').sortable('serialize');
$("#info").load("process-sortable.php?"+order);
}
});
});
</script>
HTML:
<pre>
<div id="info">Waiting for update</div>
</pre>
<ul id="test-list">
<li id="listItem_1">
<img src="arrow.png" alt="move" width="16" height="16" class="handle" />
<strong>Item 1 </strong>with a link to <a href="http://www.google.co.uk/" rel="nofollow">Google</a>
</li>
<li id="listItem_2">
<img src="arrow.png" alt="move" width="16" height="16" class="handle" />
<strong>Item 2</strong>
</li>
<li id="listItem_3">
<img src="arrow.png" alt="move" width="16" height="16" class="handle" />
<strong>Item 3</strong>
</li>
<li id="listItem_4">
<img src="arrow.png" alt="move" width="16" height="16" class="handle" />
<strong>Item 4</strong>
</li>
</ul>
<form action="process-sortable.php" method="post" name="sortables">
<input type="hidden" name="test-log" id="test-log" />
</form>
PHP:
<?php
/* This is where you would inject your sql into the database
but we're just going to format it and send it back
*/
foreach ($_GET['listItem'] as $position => $item) :
$sql[] = "UPDATE `table` SET `position` = $position WHERE `id` = $item";
endforeach;
print_r ($sql);
?>