I'd agree that FI is now probably a better choice if one can finance it after a fATPL. EGLL is probably too big an airport to develop useful contacts - and the airlines flying there will not typically consider frozen ATPL holders.
That said, over the course of 2 years, 4 dispatchers from my office got jobs with 3 airlines handled here; 3 out of 4 on heavy TPs, 1 on heavy jets. None had more than 350 hrs, 3 out of 4 didn't have to pay for a rating (they are bonded though); they (we) got interviews nearly exclusively through "on the job" networking. Being a dispatcher was also a plus at interviews, and now on the line.