I think I've figured it out. It IS a single shot with both a practical police box & a practical TARDIS set. Most likely, Alidar Jarok
is correct that the actor is walking in place while a practical police box is being rotated next to him. Then, at the last moment, the police box is placed next to the entrance of the TARDIS set and its back wall is removed, so both the actor and the camera can move unimpeded through the doors and into the set. They can pull it off because the background is just a general haze with no specific points of reference. But I'm pretty impressed that they were able to remove the back wall of the police box so quickly.