LONDON — When voters in the United Kingdom chose to leave the European Union, Britain's civil servants reacted with shock and disbelief. This was no surprise. After all, as highly educated, affluent technocrats, they pretty much check off every stereotype of a Remain supporter.

Reality is slowly setting in. As ministers head off on their summer holidays, staff in Whitehall are starting to accept that the next portion of their careers will be dominated by the implementation of a decision with which they thoroughly disagreed.

Being professionals, the question is not whether they will do it, but whether they can. Even as they knuckle down, a large question mark looms over whether a government machine shorn of so much of its former capability — and with a patchy record on major projects — will be able to cope with such significant strain.

So far, the focus has been on trade, a field in which Britain has perhaps two dozen trained negotiators, lined up against the 600 acting on behalf of the EU. Using this vestigial capacity to negotiate the myriad of trade deals that may be required will be like “trying to bail an Olympic swimming pool with a thimble,” according to one former trade adviser.

The salary of any civil servant earning more than the prime minister must be publicly disclosed. Senior trade negotiators in Brussels already earn well above that amount.

Hundreds of trade negotiators are already being recruited, alongside experts from the private sector. New Zealand has offered to loan and train staff, and there are suggestions that Australia and Canada might offer similar assistance. But it will still be difficult to find enough qualified experts, given the number of simultaneous deals that could be required. “This is complicated, incredibly technical work,” said one insider. “It isn’t like finding 300 tax collectors, it’s like finding 300 nuclear physicists.”

The draft of the trade agreement between Canada and the EU, for example, is 1,600 pages of impossibly dense technical verbiage, including obscure clauses relating to reindeer husbandry and the Saskatchewan Liquor and Gaming Authority.

One obvious place to look for experts is Brussels, in the form of Britons currently working for the EU. But luring them back to the U.K. will be tricky.

As part of an effort to cap Whitehall pay, the salary of any civil servant earning more than the prime minister must be publicly disclosed. Senior trade negotiators in Brussels already earn well above that amount — with far less scrutiny, accountability and pressure than they would face on Team Brexit. Even if their career prospects in Brussels have dimmed, how many can be lured back to fight for a cause they personally despise?

* * *

In the short term at least, there is also the problem of internal politics: the rupture caused by the creation of two new departments, for Brexit and for international trade, will inevitably result in Whitehall infighting.

Jill Rutter, program director at the Institute for Government, says the think tank cautioned against carving out completely new ministries. “If you’re really a department, you have to do lots of things that distract from your core business, like setting up your own finance system, HR system, producing an annual report, defining terms and conditions for employees. If it’s not going to last for that long, it’s potentially quite a big distraction.”

To be fair, the Brexit department appears not to have had many problems recruiting top-flight staff: In particular, its new head, Oliver Robbins, is regarded as one of Whitehall’s rising stars.

But at a lower level, many within the Foreign Office unit that deals with the technicalities of EU membership — the European Union Division Internal — are alarmed at the thought of being hived off to the new body. These are generally staff from domestic departments who have been brought over to the Foreign Office because of their in-depth policy expertise — but then often move on to pursue a diplomatic career elsewhere within the Foreign Office. That door has been shut in their face.

And it’s not only the Brexit department that will feel the demands of EU renegotiation. At a speech to the Institute for Government, Amyas Morse, head of the National Audit Office, warned that the civil service is already “over-committed” and would have to abandon projects that were not “mission-critical.”

“You’re already running two programs,” said one Whitehall insider. “There’s the ‘business as usual’ program and the ‘change' program contained in the Tory manifesto. Now, on top of that, you’ve got the biggest, most seismic change program in peacetime history. How are you going to do a seven-day NHS, 3 million apprenticeships, pensions reform, youth and childcare and prison reform, rolling out academies, cutting the deficit and Brexit, all at the same time?”

And that’s without taking into account any additional priorities set out by Theresa May and her new team of ministers.

Bob Kerslake, the former joint head of the Civil Service, already claimed that to cope with the added work, the government will need to halt planned Whitehall job cuts: Manpower has shrunk by a fifth since 2010, to the lowest levels since World War II.

* * *

At the moment, however, the cuts are set to continue: The business department, for example, is supposed to lose up to 40 percent of its headcount by 2020. “I think that’s pie in the sky, given the amount of stuff that’s got to go on,” said one civil servant. “That Steve Hilton [Cameron's former strategy director] idea of being able to fit the whole government in Somerset House — to me, that’s dead in the water.”

For Rutter of the Institute for Government, it is a question of working out how to prioritize resources. “Some departments will be very unaffected by Brexit,” she said. “But some will be profoundly affected. At my old department, Defra [which covers the environment and the countryside], all its policy agenda is affected. For example, it currently does very little legislation of its own — it’s all about bringing through EU directives.”

Agriculture is a good example of one of the likely consequences of Brexit: more British bureaucracy. In the popular imagination, the money Britain sends to the European Union — the mythical £350 million a week — is simply a sunk cost, used to pay for jacuzzis in Brussels and Strasbourg or hand-outs to avant-garde theater troupes in Riga and Nicosia. In fact, much of it comes back to Britain, in the form of grants for the regions and in particular for the agricultural system.

More pertinently, some of the spending that remains in the EU is used for shared services. In the same way that councils might outsource a particular specialized function to save money, or pool services to get the benefits of scale, Britain signed up to all manner of pan-European agencies: the European Medicines Agency, the Unified Patent Court, and several dozen more.

Yes, some of these overlap with existing British institutions. But others do not. In each case, there will be the question of whether Britain should remain part of the existing system, or set up its own, more expensive alternative — which means swelling the size of the state.

“Down the line, we may well need to start setting up big new administrative systems,” said Rutter. “For example, for registering migrants or bringing in checks at the border. What you really need to do — and what the Brexit department will be doing — is working out where the pressure will fall, and what your options are for dealing with that.”

The more Britain strikes out into the unknown, the greater the pressures on government.

Much of what happens will, inevitably, depend on the kind deal the U.K. negotiates with the EU.

A post-Brexit relationship could end up sticking closely to the status quo, simply due to bureaucratic inertia. “Under the maximal form of withdrawal, civil servants would painstakingly have to copy, or scrap, 12,295 EU regulations,” the Economist recently pointed out. “They have already started to map out every British law that derives from the EU.” All other things being equal, they will surely keep as much of that corpus as they can.

The closer the Brexit deal is to existing arrangements (in particular, over membership in the single market), the less dislocation there will be for civil servants, and for Whitehall as a whole; it's easier to copy and paste an existing law than write a new one from scratch. The more Britain strikes out into the unknown, the greater the pressures on government — and the need for more manpower — will become.

Many of those who campaigned for Brexit did so in the hope for precisely such a leap into the unknown. In some cases, they wanted to sacrifice membership in the free market in exchange for limiting free movement. In others, they wanted to restore parliamentary sovereignty and sweep away intrusive European regulation. Indeed, these people tend to be most skeptical of government’s ability to deliver, and the keenest to see it cut down to size.

Even as Brexit voters rejoice at being liberated from the bureaucrats of Brussels, they may find that power has simply been handed to the bureaucrats of Britain.

Robert Colvile is a regular contributor at POLITICO.