Under the bonnet, card hosts like Base2000 have an underlying account number for the credit facility, and various PANs (card numbers) are attached to that. Even if a singular card is cancelled, transactions posted in batch can be routed to the appropriate credit facility as the host knows all current and past PANs.
If you have subscriptions that are difficult to cancel, the best path is to ask your bank to block and/or dispute the transactions in question. Getting a new card with a new PAN may not be sufficient.