There seem to be all sorts of local government services that are withdrawn and people are not working on public facing roles but are still getting full pay. So what are they doing?
Housing officers are still dealing with tenant/estate management issues, making emergency provision for the street homeless, finding places for people fleeing domestic violence etc, planning officers are still processing planning applications, social workers are still doing safeguarding work and placing old people into care homes, finance people are still processing payments in, approving invoices for payment and running payroll, pensions teams are still doing their normal work and staff working in member services have been making sure that the council/cabinet/committees still meet to make decisions, albeit doing so electronically (which took a lot of work to set up). The bins are still being emptied, recycling collected, roads being mended, traffic signals and street lighting maintained etc. My DSS, a tree surgeon employed by a local authority is still working normally. Trees don't stop growing or getting ash die-back because of Covid! Only this morning, council workmen were cutting the grass in a park near me, and doing the verges on a nearby estate.
Off the top of my head, in my area. the only services that are not currently running are the leisure centres (run by a private company under contract to the council), the tips (ditto, and re-opening next week anyway) and libraries, who are still maintaining online services.
Many staff have been redeployed onto Covid related work. Here, there are huge numbers of people, some redeployed from other organisations, who are keeping in regular telephone contact with the most vulnerable people, arranging food parcel deliveries etc.
A lot of NHS staff are working. CPN's are delivering support to patients by telephone and monitoring their MH (and responded very promptly to a concern I raised about a mutual client yesterday), my friend who is an HCP in a GP practice is still working as are the community nurses based there. The secure MH services are working normally, they haven't just let the dangerously unwell MH people out to roam the streets! And many of their finance and other support services will be working normally, if from home.
Just because offices aren't open to the public doesn't mean people aren't working. I don't think you realise the enormous number of "back office" staff it takes to keep complex and varied public services running.