The Company has the discretion to issue tickets to the purchaser over the counter at one of its stations but will not be obliged to do so.
The purchaser is, as I understand the question, "Mum"; there is no contract with you.
I recommend that "Mum" visits one of the larger stations operated by Virgin, in person, with full identification and evidence of being the account-holder of the account which had the now destroyed card, plus the booking confirmation and evidence that the account has since been closed.
"Card B" appears to be irrelevant to the question, as is 'Mum's' new card with another bank and the 'educational relationship'.
The machines will not accept any card other than the one related to the purchase, though it is technically possible for Virgin to change that remotely so that they could be collected using another card. However, I doubt that any telephone call could provide enough evidence or persuasion to convince anyone in sales to switch the booking code to another card's ID.