`$product.cartid` --that looks like the problem to me. Just a guess from looking at your page.
I don't know how or why those little `` got in there, but I'm guessing that's the issue.
When you view the source of the page, line 188. It should look like this:
<a class="simple-button simple-delete-button" href="cart.php?mode=delete&productindex=1" title="Delete item"><span>Delete item</span></a>
Yours looks like this:
<a additional_button_class="simple-delete-button" style="link" href="cart.php?mode=delete&productindex=`$prod uct.cartid`"><img border="0" src="http://www.signaturecardcompany.co.uk/xcart/DeleteItem.jpg"></a>
In yours the product index is not being assigned to the delete button.