A lack of resources in Whitehall threatens the UK's successful exit from the EU, the head of the senior civil servants' union has warned.
Brexit will mean a cut in public spending unless funding is increased, the First Division Association says.
A Conservative MP who voted to leave the EU warned the work could take two decades to complete without more support from ministers.
The government said it would deliver Brexit.
Dave Penman, the general secretary of the FDA, which represents senior civil servants, said the government could not demand that civil servants deliver public services, cuts to budgets and Brexit at the same time within current budgets.
He told BBC Radio 4's Today programme the success of exit from the EU was threatened if it was not adequately resourced.
He said: "If you take those resources from elsewhere within government spending, it threatens the delivery of public services.
"That's the reality: you can't have your cake and eat it."
Departments whose budgets are not protected are set to have saved almost a third of their day-to-day spending by the end of this decade, according to the Institute for Fiscal Studies.
Cuts for the next four years were made at the Spending Review in November, before the EU referendum.
Mr Penman says the funding settlement should be reconsidered in the light of the Brexit vote.
He said staff at the Department for Exiting the European Union had been told it was not expected to exist in two-and-a-half years, once the UK has left the EU.
And he argued there would be a huge new task for the rest of Whitehall to then decide which EU regulations should be retained in British law and which rewritten or rejected.
He said without more resources, "Brexit will simply mean a further cut in public spending - because departments will have to cut other work to deliver the resources that are required to support the new policy areas or support the negotiating process itself."
The Conservative MP Stephen Phillips, who voted to leave the EU, said: "Rather than being the work of two years, I fear it may actually be the work of two decades unless we devote considerably more resources than the government appears to be doing at the moment to the task."
He said ministers were doing good work to deliver new trade deals, but said "there may not be an appreciation in government of quite how large this task is going to be".
A government spokeswoman said: "We have put the machinery of government behind leaving the European Union and making a success of it.
"This includes a dedicated Department for Exiting the European Union, and a Department for International Trade.
"This government is going to deliver on the national mandate for Brexit and we will deliver it in the national interest."