Wish I lived so near that many Police Boxes! Anyway, your Logopolis reference got me thinking:
It would have been a lot of work for a gag, but it would have been fun (and funny) to see The Master turn up with a Tardis looking like a Glasgow box - especially if it was in its original red livery! ;D
Now I'm also thinking: in the Whoniverse - without a popular TV show to firmly plant blue boxes in the hearts of millions - would the Glasgow boxes have been a) Preserved, and b) so often re-painted blue?