A period of uncertainty over political leadership after the announcement that David Cameron would quit has not made the mandarins' lives any easier. One familiar and important issue has bubbled up to the surface again - NHS finances.
The fraught task of finalising the Department of Health's accounts for the last financial year is close to completion. Sources indicate it's touch and go as to whether the department kept to its spending limit agreed by parliament for the health service in England.
An overspend would be a serious breach of Whitehall protocol and lead to senior officials being hauled over the coals by the National Audit Office.
Ministers and the leadership of the NHS in England are determined to demonstrate they have got a grip on the finances. To that end, a major initiative is planned involving commitments by all trusts in England to stick to agreed spending limits.
The regulator, NHS Improvement, under pressure from the government, is straining every sinew to bring down the Â£2.4bn total deficit racked up by trusts in the last financial year. Putting finance directors' feet to the fire and extracting pledges to stay on budget has been the priority in recent weeks.
The NHS financial announcement is likely next week and could well come on the same day as the publication of the Department of Health accounts. The government line will be that running up unplanned deficits and risking breaches of limits set by parliament will be no longer acceptable.
At a conference organised by the Reform think tank, the Health Secretary Jeremy Hunt talked of the need to "restore financial discipline".
He said that trusts should not assume there was a choice between maintaining patient care standards and controlling their finances and that the two were not incompatible. Mr Hunt argued that the hospital trusts with the best ratings by the Care Quality Commission tended to be those with the lowest deficits.
But announcing commitments to prudent spending is one thing, delivering them is another.  Once winter and the second half of the financial year arrives, the pressures will mount.
It's hard to see what sanctions can be applied to trust managements who feel they have to go over their agreed budgets to meet relentlessly increasing demand for patient care.
At some hospital trusts, the inevitable consequence of sticking to agreed spending totals will be longer waiting lists.
Looking longer term, the referendum has raised more questions about the sustainability of NHS finances.
The head of NHS England, Simon Stevens, has called for politicians from either side of the referendum campaign to ensure that pledges for a better funded NHS made during the campaign are delivered. But it will be harder to hold out the begging bowl to the Treasury.
The Health Foundation think tank has pointed out that the public finances will be under even greater pressure with economists revising down short-term economic growth forecasts in the wake of the Brexit vote.
Anita Charlesworth of the Foundation made the point that when the economy sneezes the NHS catches cold and that the service's finances were already "in a truly dire state".
Ministers argue that the government has already made a significant commitment to funding above the rate of inflation for the NHS at a time when other parts of Whitehall are being severely squeezed.
They say that making better use of resources, through greater efficiency, is well within the capability of most trusts. But as the NHS celebrates its 68th birthday, the question marks over financial sustainability are perhaps as big as they ever have been.
How things will look when the service celebrates its landmark 70th anniversary is anyone's guess.
After prolonged debate during the referendum, Whitehall has been busy since polling day trying to work out the implications of Brexit - including how the NHS could be affected.