The RHA said there was already a backlog of 50,000 HGV licences following the pandemic and any further strike action would worsen the situation.
Meanwhile, ministers have previously criticised the union for “politicising” the death of Mr Grant even after the HSE’s findings.
Appearing before the parliamentary committee in July, Baroness Vere, the roads minister, said the HSE had found “nothing was amiss” with the DVLA’s Covid controls at the time of the worker’s death. She added: “It is therefore wrong and possibly hurtful to the family to keep mentioning that death and I find it very upsetting.”
The latest strike threat comes after a potential deal between the PCS and the Government to get DVLA staff back to work broke down earlier this year. The union has previously said that only between 250 and 500 of the DVLA’s 2,500 staff need to be working in its offices.
The PCS accused ministers of “scuppering” an agreement in June which would have seen the agency’s staff return to work and each be paid £200 in recognition of their hard work during the pandemic.
However Baroness Vere has said negotiations collapsed after the union demanded extra pay and bonuses in a dispute that was nominally about health and safety concerns. She said the new pay demands equated to “not so much moving the goalposts but changing the sport”.