Untitled

You can do something like:
# mkfifo url.list ; while sleep 1; do wget -i url.list; done

like that wget will indefinitely be waiting around to be fed with URLs and download them automatically as soon as they arrive

You can quickly test it's working by sending it download URLs from another terminal:
# url='http://yourpornoranything.com/get.php?file=/xyz.part01.rar'
# echo $url > url.list

OK now you need a way to feed it with URLs from a remote browser. Not a problem.  Just install some minimal webserver + PHP and create 2 following files at your www directory :

index.html
~ ~ ~
<html>
     <head>
      <title>My Download Tool</title>
     </head>
     <body>
        <form action="action.php" method="post">
          Please enter URL:<br>
          <input type="text" name="url"><br>
           <input type="submit" value="Submit">
        </form>
     </body>
    </html>
~ ~ ~

action.php

~ ~ ~
<?php
 $path = 'url.list';
 if (isset($_POST['url'])) {
    $fh = fopen($path,"a+");
    $string = $_POST['url'];
    fwrite($fh,$string); // Write information to the file
    fclose($fh); // Close the file
 }
?>
~ ~ ~

Then just open your VPS IP in a browser tab and fill the box with your desired download URL every time.

* this is just a quick example sent from smartphone not tested sorry if any stupid error but safe to try ;)

* once you got the idea,  pipe (a special file) name 'url.list' should also be used at your www directory so full path should be used in variable, so edit accordingly

* you may find ways to automate it further (perhaps using AutoHotKey? )