According to the DVLA web site (
https://www.gov.uk/vehicle-exempt-from-vehicle-tax ) at the moment:
"Vehicles made before 1 January 1978 are exempt from 1 April 2018."
Unless anything changes between now and then, on 1st April 2019 I would expect that would change to
"Vehicles made before 1 January 1979 are exempt from 1 April 2019."
So as I read it, the only way your April '79 vehicle will become VED exempt this year will be if you can prove it was manufactured before 1 January '79, not 1 April '79. And if the change in date means that your vehicle should have an earlier registration suffix, the DVLA may choose to give you a replacement registration to match the manufacture date.