My suggestion is the time machine trunks uses in Dragon Ball Z 

I am not just suggesting it because its a time machine but because of some dragon ball abridged episodes where the time machine has Tardis sounds and is (doctor who like?) whether its got the default sounds or the ones from dbz it would fit well and since there's exteriors like the  green pipe and porta potty I don't see why not. 

plus the bill and ted phone box is also from another franchise (me justifying it)

you would get in by opening the top like in the show however having the shrinking into a capsule aspect would be  cool?

open:

closed:

misc:

Dragon ball is my second favourite franchise if you couldn't tell 

and here's what inspired me https://youtu.be/yyN7rPbHybk?list=PL6EC7B047181AD013&t=480