Civil servants working for Angela Rayner launched indefinite industrial action on Monday in a dispute over issues including office closures and a ban on working from home.
Members of the Public and Commercial Services union (PCS) at the Ministry of Housing, Communities and Local Government based in offices including London are taking action short of a strike.
The PCS said indefinite “work to rule” action was starting on Monday.
The union said it is campaigning against the closure of six offices, the imposition of "rigid" office attendance policies, and the withdrawal of location-neutral recruitment.
Employees at the Ministry of Housing, Communities and Local Government (MHCLG) are understood to be particularly upset by the working from home ban because Ms Rayner has led Labour’s workers’ reforms, which will include the right to request flexible working.
PCS president Martin Cavanagh said: "From removing staff from an office before the lease expires to spuriously challenging lawful notices of industrial action, the employer seems intent to avoid proper consultation, disregard fair process and alienate its staff.
"Closing local offices while rigidly enforcing mandatory office attendance doesn't make sense. The way out of this dispute is to negotiate, not frustrate."
A Ministry of Housing, Communities and Local Government spokesperson said: "We have engaged with unions and staff about a number of proposals - including plans to expand four offices outside of London and close six offices over the next two years, as leases come to an end.
"The department will continue to have offices in every English region as well as Scotland, Wales and Northern Ireland and all staff affected will be able to continue in their roles."
The Conservative Party's Alex Burghart, shadow chancellor of the duchy of Lancaster, said: "It speaks volumes that some civil servants are walking out not over pay, but because they're being asked to show up to work and make better use of public buildings.
"Most people can't refuse to travel to their workplace, so why should Whitehall be any different?
"Labour should be clear whether they stand with the unions defending empty desks or with taxpayers who expect a civil service that works for them."
