When I call the wiki APIs to access image URLs, I get image URLs like this,
File:Ad-tech London 2010 (2).JPG
How to get the correct URL for this file from the wiki API?
You can get property URLs from an imageinfo request, for example:
https://en.wikipedia.org/w/api.php?action=query&titles=File:Test.jpg&prop=imageinfo&iilimit=50&iiend=2007-12-31T23:59:59Z&iiprop=timestamp|user|url
See the MediaWiki API Help for more information.
There's a little documentation on image / thumbnail URLs other than T153497 . You can use Special:FilePath and / or thumb.php :
Special:FilePath
thumb.php