Blocks page and Themekey module I am referring to this page.

I need to use the administration theme on this page, but this is blocked by default.

At the moment I have to go to the theme page, change to my admin theme, and then change back when I have made the changes I need.

Is there anyway I can set this up using the Themekey module? It is beginning to be a major problem for my client.
No, there is no way you can change theme on this location using themekey. 

You might consider to do this in your custom module. Something like this:

function YOUR_MODULE_NAME_init()
{
  global $custom_theme;
  if($_GET['q'] == 'admin/build/blocks'){
    $custom_theme = 'your_theme_name';
  }
}