You need to check the terms and conditions of the insurance company re penalties before you do anything, and then contact www.citizensadvice.org.uk - they are usually very helpful.
Of course the company can't keep helping themselves from her bank account. It isn't as easy to cancel 'continuous payments' on debit or credit cards as it is 'direct debits' on bank accounts, but her bank should have advised her about that. They would need to cancel her present card and issue her with another, with a different number, which should take only a few days.
Direct Debits are OK - they can be cancelled at the click of a mouse on your online banking or in a branch. Continuous Payments can't, the bank doesn't have a record of those even if it's on their debit card, so don't use them!
When an insurance company finds that a payment has been failed, they usually contact the policy holder and tell him that the policy will be cancelled if he doesn't come up with an alternative source of payment within (probably) 14 days.
The only problem might be a penalty for the rejected payment. You need to be sure that it will be the policyholder who gets clobbered and not the cardholder, which is why you should contact the CAB first. It is unlikely that you will get any refund unless the CAB say that the fact that the company was advised that the van had changed hands, or that the bank did not advise as they should have, carries any weight.
Good luck!