Hmm, I think it's a Nokia 

http://www.dailymail.co.uk/news/article-2301996/Was-worlds-mobile-phone-1938-film-shows-woman-talking-wireless-device-time-travel-family-say-disappointment-conspiracy-theorists.html

If it was a cell phone, where were the satellites and masts ?   

All you need is a TARDIS. It works on Doctor Who!

Weird video though. Assuming it isn't a mobile phone, what do you think it is?

Ahh yeah, I had forgotten about the TARDIS, well that's solved that one then, the power of the Datahopa Think Tank strikes again 

If you look closely at the image of the video above, I think the woman on the right of the one with the cell phone is the Doctor in drag.

I could be wrong though. 

Can't be the Dr. (s)he would have to look cooler than that in drag. Besides, dressed up or not, where's the bow-tie?