Brexit will add to the strain on a civil service already struggling to cope with major projects, the National Audit Office has found.
The spending watchdog said weaknesses in capability in Whitehall undermined the Government's ability to achieve its objectives.
Leaving the European Union will "further increase the capability challenges" facing the Government, as officials take on responsibilities previously handled in Brussels.
The pressures of Brexit come on top of a "challenging portfolio" of major projects such as the Hinkley Point C nuclear power plant, HS2 high-speed rail and the renewal of the Trident nuclear deterrent.
"Government projects too often go ahead without government knowing whether departments have the skills to deliver them," the report warned.
It suggested that projects should be prioritised, with the Government halting schemes that "it is not confident it has the capacity to deliver".
The report said that although there had been improvements in how some departments manage programmes "we continue to report regularly on troubled projects" and "many delivery problems can be traced to weaknesses in capability".
The NAO said the Government needed to show "greater urgency" in filling skills gaps in Whitehall.
The report said: "Government is facing ever-increasing challenges in providing public services. Continuing budgetary restraint is putting pressure on departments, which are already managing important reforms with fewer staff and smaller budgets.
"The decision to leave the EU also means government will have to take on tasks previously undertaken by others, requiring the development of skills not previously planned for."
The report noted that a third of the roles in the Department for Exiting the EU and the Department for International Trade had not been filled as of February.
A thousand new roles had been created but only "two-thirds of the roles have been filled, mostly by transferring staff from elsewhere in government".
It acknowledged that ministers had accepted the need to do more on workforce planning but "progress so far has been slower than the growth in the challenges the civil service is facing".
The report suggested that the Government will need to spend at least £145 million a year to hire the 2,000 additional staff with digital skills required within five years.
Other shortage areas included commercial and project delivery skills, the report said.
NAO chief Amyas Morse said: "The civil service is facing ever-increasing challenges.
"The work of government is becoming more technical, continuing budgetary restraint is putting pressure on departments and the decision to leave the EU means government will have to develop new skills and take on work previously done by others.
"Government has gaps in its capability and knows it must do more to develop the skills it needs. It is making plans to do so but the scale of the challenge ahead means greater urgency is needed.
"Without a short-term solution to its capability gaps, government must get better at planning and prioritising its activities and be prepared to stop work on those it is not confident it has the capability to deliver."
Head of the civil service Sir Jeremy Heywood said: "The UK is well placed to deal with the challenges, and take advantage of the opportunities, that lie ahead as we prepare for Brexit.
"We are focused on delivering this Government's commitment to leave the EU and get the very best deal for the UK. We are equipping ourselves with the right people and the right skills across government to make this happen.
"At the same time, the civil service is also working hard to make sure that all the priorities of the Government are being delivered."