Workers at the Driver and Vehicle Licensing Agency (DVLA) have begun a four-day strike.
Members of the Public and Commercial Services (PCS) union at the Swansea offices walked out on Tuesday in a dispute over Covid-related safety.
They want fewer staff to have to go into the office following a Covid outbreak there last year.
A DVLA spokesman said Covid cases among staff remained very low and it was following Welsh government guidance.
The industrial action comes after workers at the site voted to strike last month.
It was prompted after Public Health Wales said just before Christmas there had been 352 cases of Covid-19 at the centre at Swansea Vale in Llansamlet since September.
The union said despite extensive negotiations to resolve the dispute, the DVLA was insisting more than 2,000 people had to go into the Swansea office every day.
'Fear and anger'
PCS general secretary Mark Serwotka said: "It is the unreasonable and crass behaviour of DVLA senior management which has led to the latest round of stoppages.
"DVLA and ministers need to understand the levels of fear, anger and determination within the workplace and that our union will support staff every step of the way in their fight for a just settlement."
A DVLA spokesman said it was disappointing the PCS was pushing ahead for a second round of industrial action, adding cases of Covid-19 among staff remained very low.
"DVLA has ensured that it has followed Welsh government guidance at every single point throughout the pandemic having consistently worked with Public Health Wales, Environmental Health and Swansea Bay Health Board to introduce a wide range of safety measures," he said.
"This has enabled DVLA staff to continue to deliver essential services to the public right across the UK in a Covid-19 secure way.
"DVLA's online services will operate as normal during this period of strike action and we advise customers to use those wherever possible.
"Those posting paper applications to DVLA or trying to reach our contact centre are likely to experience delays."