Which airlines would those be? Only I'm make sure not to apply and waste everyones time trying to work for a small minded bunch. I've heard recruiters say they don't care, it's the licence that matters. So if you could tell us then it would save people from troubling the integrated airlines
The BALPA careers website has statements from recruitment departments of various airlines outlining the requirements and giving advice etc.
The following airlines state that they will only consider low hours pilots from an integrated background: BA, Emirates,Excel,GB and flyBE. And BAC Express and Ryan Air express a preference to those from an integrated background.
How much this is adhered to i don't know, especially as you have heard otherwise but there you have it....