Did you follow the correct process, it sounds like you asked Sky to disconnect the line?
Correct process, Ring BT or Place order on BTs website, provide them the Sky landline number, let BT handle everything. Do not ring or speak with Sky. When BT take-over, they notify Sky and a final bill is generated.
If you ring Sky to cancel at any stage, they will close the line down entirely, meaning there is no line for BT to take-over on the move date - which is what it sounds like has happened. Am I right?