A fraudulant or erronous transaction.
Reversing a charge for any reason, initiated by the Issuer (the bank which issued the card), usually on behalf of the card holder. The money is refunded by the Acquirer (bank which provides the merchant with card payment facilities). The Acquirer will likely claw it back from the Merchant, but that's their business and outside the chargeback mechanism. There are very strict rules which banks sign up to when they become Visa/Mastercard Issuers or Acquirers about under what circumstances they can perform a chargeback. There's also a "representation" (reversing a chargeback by the Acquirer), although that can be subject to a chargeback too.
Note that your Issuer will have to refund you under some circumstances without performing a chargeback (in which case they take the hit). If a chargeback happens, then the Acquirer or the Merchant will take the hit, but it would have to be a circumstance where a chargeback was permitted. If the Issuer and the Acquirer disagree, then they have to pay for the Processor of the transaction (Visa or Mastercard) to perform dispute resolution. This however is just between the Issuer and the Acquirer, and does not affect you -- if the Issuer has gone that far then they've already refunded you and it's just a question of them being refunded or not by the Acquirer. Generally, you will have no idea if a refund was paid for by your Issuer or by a chargeback (hence the Acquirer or Merchant).
I'm not up to date with the exact situations in which chargebacks are allowed, but I don't think most of the likely issues under the Consumer Credit Act protection would count, once the goods have been received, and there's a time limit on chargebacks anyway which way shorter than time you might take action under the Consumer Credit Act. Non-receipt of goods is however a valid reason for a chargeback. Chargeback rules are international, whereas the Consumer Credit Act isn't, so an Acquirer or Merchant (who might be international) has no obligation under the Consumer Credit Act, whereas the Issuer does, as they're the ones providing you with credit.