A disturbing lack of phones in the latest series of Doctor Who - and no news yet on the next series. So let's revisit an older episode I'd previously overlooked.
"Midnight" is a Series 4 episode which has a terrifying sequel in this year's "The Well".
Donna briefly has a chat with The Doctor on what a appears to be a landline phone with the wire removed.

Obviously that's not a mobile phone.
But what's The Doctor speaking to her on?
A payphone? Look a little closer:

A rotary dial payphone!
This is the the Coin Telephone 725A. Isn't it gorgeous?

But is it a mobile phone? Yes. Yes it is. The Post Office Telecommunications Bulletin DLE 530 describes this as "portable with plug and socket termination".
How portable? Easy to lug over a bar.

And light enough for a dainty lady to carry.

So, there you go, a sort of mobile phone hidden away on the Planet Midnight!
You can read dozens of these very silly blog posts in the archives.