The instructions for the "new" V5C still, under the "scrapping" section, still include the words "until you tell us" ... so AFAIK .... all you have to do is tell them, in writing...... 
Seems like a simple letter will do .... 
and from the DVLA website .. same message / different words ..
http://www.direct.gov.uk/en/Motoring/OwningAVehicle/ChangesToYourRegistrationCertificate/DG_4022057
"If you have broken up the vehicle yourself, you must either continue to tax it or tell the DVLA that you are keeping it off the public road. You can do this by making a SORN (Statutory Off Road Notification). You will need to make a SORN every year until you have taken it to an ATF, or told DVLA that you longer have it."
Yes, I think that could have been worded better.
In the context of this proviso;
You must take your vehicle to an authorised treatment facility (ATF) if it needs to be scrapped. it seems that there is little room for DIY scrapping and where the words
or told DVLA that you longer have it are concerned I would imagine if the DVA were informed that a registered keeper no longer had the vehicle they (DVA) would seek details of the new keeper.
Should they then be informed that there was no new keeper due to the vehicle being scrapped they would then require an ATF certificate to finalise the former keeper’s interest in it and responsibility for it.