What are the penalties if I don't notify DVLA?

The Certificate of Destruction from CarTakeBack and written confirmation from DVLA (which you should receive if you've notified DVLA yourself) are both proof that DVLA have been notified correctly.

If DVLA records are not updated correctly, you could get an £80 fine, be liable for any traffic offence penalties carried out in the car, as well as for paying tax in arrears, County Court Judgements, a fine of £1,000 and even be liable to prosecution.