If we request the MAC while still being in the minimum contract time, would we have to pay the cancel charge even if we actually moved AFTER the contract has ended?
No. (But don't confuse the end of the minimum term with the totally different
Broadband Cease. That would take a while to explain and doesn't matter here and now).
The request of a MAC does not mean you will necessarily be leaving. If you don't use it, it just lapses. Though with some ISPs, if it is taken as the start of notice, you need to tell them you are staying.
In your case it is fine to ask for it, as long as the actual leaving date is after the end of your minimum term. It would probably be best to wait until you are within a four of five days of then, so there is no possibility of you being moved to Sky before the end of your BT term, as that could trigger a charge for early ending of the contract.
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