I am not an expert but I have been listening to the hubbub in these areas for quite some time. I have also had the pleasure of chatting first hand to a couple of UK based airlines, this has included newly recruited pilots and the chaps and ladies involved in the recruitment process. I'm sorry to say that the hymn sheet definitely reads "one training provider".
I can't imagine this is a set rule (I know of a chap flying for a UK airline, low hours and different modular schools), I'm just saying that if you do have the choice, even if it involves a bit of extra cash saving then try and stick to one place.
Best of luck
Camel Toe
"Over Macho Grande?"