You are normally looking at about 1 month to complete the move.
The time span really varies, depending on the losing supplier being forthcoming with information and not raising objections to the move, which can and does happen.
You can normally obtain quotes up to 3 months (sometimes longer) in advance of your existing contract finishing, so we would normally advise looking about 2 months before your contract ends, giving you plenty of time to find a new supplier and get the move completed when your contract finishes with your old supplier.