In my experience it's always a huge headache to migrate. I know I had a hell of a time migrating my dad's service a few years ago. He's just migrated again, from Demon to BT, strangely this time with no problems! Was connected within a week. I was quite surprised actually, not because BT are a nightmare, all of my family including myself have been with BT for years without a problem, but because he asked me to check out BT for him, and had it done before I could even get him details on their packages!
Doesn't seem to matter who you're leaving though or who you're going to for the most part, migration is always a headache. But what a lot of folks on here are forgetting it seems, or merely not stating is that BT provide the line rental for almost every internet company in the UK, whether they state it or not. They should state it but a lot don't. That's ISPs, not the fellow forum goers...so that does mean you'll have to give BT line rental back. Hopefully this will change one day though and BT will not have such a stranglehold over the UK and we'll all have the choice we're entitled to.