Flybe minimum requirement (on their website) is 50 hours in the past 6 or 12 months - can't remember which. They don't care whether its FI or 737 time as long as you have it.
50 hours btw in the UK will cost you about the same as an FI rating if you were to hire from a club and do it that way.
So there is one at least. When it comes to an interview, 500 hours of FI would probably put you in a better position than 500 hours of bimbling.
...course 50 737 hours probably trumps FI hours in the interview!