It is always the seller's responsibility to inform DVLA no matter you sell your car privately or sell it to a motor trader. You should not give the whole V5C to your motor trader even if you are asked to. Fill the section 9 of V5C and send it to DVLA, Swansea, SA99 1BD. You can give the rest of V5C to the motor trader.

If you have already given the V5C to the motor trader, you still can send DVLA a letter saying that you have sold the car. You need to include the car registration number, transaction day, the name and address of the motor trader.

If your motor trader had sent the form, you should get a confirmation letter from DVLA within 4 weeks. If not, you should contact DVLA or file a complaint online.

For more, check here.