You are looking at the HTML representation of the XML format.
HTML is good for debugging, but is unsuitable for application use.
Specify the format parameter to change the output format.
To see the non HTML representation of the XML format, set format=xml.
See the complete documentation, or API help for more information. 
<?xml version="1.0"?>
<api>
  <query-continue>
    <alllinks galcontinue="Barnsley_Irish_Dance_Academy|1538" />
  </query-continue>
  <query>
    <pages>
      <page pageid="1380" ns="0" title="Dancing in USA" />
      <page pageid="1484" ns="0" title="Dancing in Ireland" />
      <page pageid="1538" ns="0" title="Dancing in England" />
      <page pageid="3308" ns="0" title="Dancing in Mainland Europe" />
      <page pageid="4690" ns="0" title="Defunct/Merged Schools" />
      <page pageid="5481" ns="0" title="Reel Fit Fun Irish Dance" />
    </pages>
  </query>
</api>