The UK government - Shapps is the one in charge, and they are responsible for having failed to make it safe for those DVLA workers who need to come in to do so.
I know very little about the work of the DVLA, not being a driver, but was it really not possible for the processing of driving licence applications to be paused? If DVLA staff aren't able to be safe at work they should be furloughed at 100% and all non-essential operations paused. A contingency plan should have been drawn up by the Department for Transport and all government departments when the first cases were discovered in Wuhan to look at how government departments could work safely.
COVID rules are clearly being breached according to the Guardian article:
Lewis, who has had to self-isolate six times, said contact centre staff were not able to wear masks and were sitting close together. “We sit back-to-back, just one metre apart,” he said. “They say ‘the two-metre rule only applies if you’re face to face’.”
The initial results of a survey of more than 700 Swansea DVLA workers by Prof Phil Taylor of the University of Strathclyde reveals nearly 70% are less than two metres from those seated in front of them and just over 20% are less than two metres from colleagues seated next to them.
The UK government are also responsible for the failure to invest in a computer system that would allow more DVLA staff to work from home.