Sarenco pretty much sums it up, plenty of commercial lending happens this way though.
I moved to Ireland from UK in 2007, I had a mortgage on my UK home with Halifax in the UK. At this time Halifax were just opening, in what turned out to be a very short stay, in Ireland, under the BOSI umbrella and, though I was a good customer and they were keen for new business, Halifax UK could not just transfer my debt to be secured against Irish collateral.
Different markets with (as we can see quite clearly) different margins and different risks. You won't even get a northern bank lending cross-border. And, obviously, with UK there are potential currency issues also.