I am looking to find the parent div id (i.e. \"Bakerloo\") from this layout when the button is clicked within \".buttonleft0\" in jquery / javascript.
alert($(this).parent().id);
If you want to be sure to select correct class, try:
alert($(this).parent('.div').id);
If you have a deeper hierarchy you can use:
alert($(this).parents('.div:eq(n)').id);
where n is which parent you want to get