I just think its a compromise between time and money. A PhD in Communication at Columbia would take atleast 2 or maybe 3 (if you don't have a Master's), while an MSc from LSE would take a year. Since you don't have funding for LSE its going to cost you not 25k but atleast twice that if you include living expenses, while on the other hand your PhD is fully funded.
And then there is the question of your career aspirations. If you want to continue with your journalism career, a PhD from Columbia J School will in my opinion be looked at quite favorably. An MSc in History of IR from LSE won't hurt but I'm not sure how it'll help in furthering your career in journalism plus it'll cost you 50k, but then maybe you're interested in international reporting or something like that, so you could make that work too. It's like I said a compromise between time and money. Good luck with your decision, I hope I was able to help out.