This is mostly a topology question. For simpler examples, you might take a look at a Moebius strip or a Klein bottle.
It's difficult to explain, our brain circuitry has evolved to understand mundane 3d space and doesn't deal well with such things. But the big blue police box would just be sitting there in the control room, with the exit door twisting back in on itself to open back up inside. It seems like this shouldn't be possible (and it probably isn't, we are talking about fiction after all), but if one region of space doesn't need to connect to the adjacent region of space, then there is nothing that should prevent such a thing.
Presumably, this would mean that the TARDIS is still in whatever time/space that it was before you put the exit/police-box inside of it (and, that it can travel to other locations and times even in this state). So if he had piloted it to London in 1968, it would still be there, though to the people of London it would be invisible.
It would clearly lack an entrance for the people of London to enter it. It may or may not lack an exit for the Doctor and his companions to leave into London. On that last one, I get the distinct impression that the insides of the TARDIS are vast, maybe a few square kilometers of livable space, so who can say whether there are other exits? If there are, and one was used, I would expect that they would have a much more spectacular appearance from the perspective of those outside. They'd just see a borderless portal open in the middle of the air.
If such is correct, then that would be the solution to fixing such a problem... they'd pick up the police box and cart it out through another door.