"do UK airlines prefer you to be trained in UK schools, or is any JAA state school fine?"
Well, a recruiting representitive / captain / whatever from flybe told me that it didn't matter to him. He would take low hour pilots from any JAA integrated school. The guy from B.A. said that he had to "recognise" the school (he didn't recognise the Australian integrated school i asked him about)
Many application forms ask which country your license was issued from.
I'm at Jerez, the license is issued in the UK and the airlines "recognise" the school. I love it here, I have no regrets about coming here. But you've got to make up your own mind "which school is right for you".