Staff at the agency’s Swansea office are staging a four-day strike, with drivers warned to expect delays to postal and phone applications for matters such as renewing licences and changes in vehicle ownership.
The Public and Commercial Services (PCS) union said the strike, which will run from Wednesday 2 June until Saturday 5, was the first phase in "sustained and targeted" industrial unrest planned for coming months.
The strike relates to the number of staff required to go into the Swansea offices. The site was at the centre of a Covid outbreak last year and the union has demanded that fewer staff should have to attend the office and called for better protection for vulnerable workers.
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The DVLA says it has followed Welsh Government advice at every stage and done everything it can to keep staff safe.
PCS general secretary Mark Serwotka said the two sides had been close to agreeing a deal to end the dispute but claimed it was suddenly withdrawn at the 11th hour without any explanation.
He said: "Through painstaking negotiation, our union and DVLA senior management were on the verge of agreeing a deal only for it to be scuppered at the last minute.
"We strongly suspect senior ministers at the Department for Transport have interfered with the progress we were making and want to make some kind of ideological stand against PCS.
"They have grossly underestimated the resolve of our members in DVLA and have only emboldened them to take targeted and sustained action in the months ahead until they win.
"PCS is fully prepared for months of strike action, and we urge the Government to rethink its position."
A DVLA spokesperson insisted that only staff who could not work from home were required to go into the office and that staff safety was its main priority. They said: “It’s disappointing to see the Public and Commercial Services union not only choose to continue with industrial action when there are zero Covid cases at DVLA, but they are also specifically targeting areas of the organisation that will have the greatest negative impact on the public, including some of the more vulnerable people in society, just as restrictions are starting to ease.
"The DVLA has worked closely with Public Health Wales along with Swansea Environmental Health and the Health and Safety Executive who have conducted regular site visits and inspections and have repeatedly confirmed a high level of compliance with control measures.
“Millions of people right across the UK are relying on essential DVLA services and PCS’s demands will cause significant and unnecessary disruption to families and businesses, all at a time when they are most needed.”