I think it's fair to say that in the UK significantly changing a timeslot for a show (other than a one-off for a sporting event say) is pretty rare. A show has to pretty much get a confirmed zero viewers before stuff like that happens. There have been a couple of shows in recent memory I think, but it's still seems pretty rare.

Even rarer is a series being cancelled mid-showing. Usually if a series is unpopular it's simply not renewed at the end of it's run. The only example I can think of off the top of my head was a show called Bugs. It barely survived the chop at the end of it's third series (each one weighing in a massive 10 ep's each). But in the last season it got canned with 3 ep's to go and the remainder didn't Tx until a year later.