It's not generally possible unless specifically supported in some way by your browser, but you can create bookmarklets in JavaScript that add image title text to the web page as regular text paragraphs. How well that works depends on the layout of the web page.
One possible implementation is the following as URL of a bookmark:
javascript:(function(){for(var i=0;i<document.images.length;i++){var t=document.createTextNode(document.images[i].title); document.images[i].parentNode.insertBefore(t, document.images[i].nextSibling);}})();
This will add the image title text just after every image on the web page. For XKCD, it looks like this:

It's not easy to type on iOS, but you can use iCloud to sync it between desktop and iOS device.