These moves are a pain, aren't they?
Twice in the past I have been offered a better deal by the company I was leaving, when the cooling-off period had come and gone! The first time, I managed to wriggle out of the switch because the company I was supposed to be moving to (through a compare website) hadn't even bothered to contact me in any way, shape or form some month or more after I'd supposedly set things in motion, and the second time I angrily told the company I was leaving that if they had a better deal to offer me, they should have offered it in the first place. 
If I find a better deal elsewhere, I will have a dilemma: if I set the change in motion too soon I risk being moved before my current good deal comes to an end, but if I wait until near the time I risk being put on the current supplier's expensive tariff for a couple of months. I am almost certain to lose out one way or the other!
Grrr, why do they make life so difficult?