Will I get any penalties if I don't notify DVLA?

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

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.