Civil servants will be pushed “to the limit” by Brexit and more officials will need to be drafted into Whitehall to cope with the workload during two years of departure negotiations, according to expert analysis.

A joint report by the Institute for Government (IfG) and UK in a Changing Europe thinktanks also suggests Whitehall will need clear direction on what projects can be “delayed or dropped” to free up resources for Brexit.

Increased spending in ministries such as the Home Office and Department for Environment, Food and Rural Affairs (Defra) is said to be “inevitable” in the research.

“When the prime minister triggers article 50, pressure on the civil service will intensify as the countdown to exit starts,” said the IfG programme director, Jill Rutter. “The government’s focus will quickly shift from preparing for talks to managing negotiations and laying the foundations for life outside the EU.

“With limited time and capacity, the pressure on ministers and the civil servants supporting them will increase. Successfully delivering Brexit in this context will require agility, leadership and realism.”

The paper says Brexit will place four key demands on the civil service: analysis, coordination, legislation and delivery. It praised the government for speedily setting up two new departments but suggested civil servants were currently working on the tip of the iceberg.

The Department for International Trade (DfIT) is already headhunting a new senior adviser, the study noted, but it also needs a “strong legal team” to negotiate deals with non-EU member states.

“The pressure of Brexit will be felt right across government and delivering it alongside existing commitments will test capacity to the limit,” said Prof Anand Menon, director of the UK in a Changing Europe.

“The civil service has many of the core skills required to do the task but effectively managing competing priorities and limited resources will require strong leadership.”

The report also said the government would need to retain all its staff and new recruits until the 11th hour of the two-year exiting period to “manage last-minute changes”, suggesting a significant increase in the number of civil servants employed for the remainder of the parliament.

It reads: “In order to free up capacity for future stages of Brexit, departments need a steer from the government as to what policies can be delayed or dropped.

“In other areas, the amount of work is such that reprioritisation alone will not work – it appears inevitable that the government will have to revise the spending plans of departments such as Defra and the Home Office.”

The study follows a leaked memo claiming Whitehall was working on more than 500 projects relating to leaving the EU and would need to hire 30,000 extra civil servants.

The FDA general secretary, Dave Penman, the most senior union official representing civil servants, followed up by saying Brexit posed the single biggest task to the UK’s civil service since the second world war.

The prime minister, Theresa May, was slammed in the weekend’s newspapers for being “ill prepared” and having no plan B in case Brexit negotiations fall apart.

The experts’ report, released on Monday before a live-streamed debate at 5.30pm, did not pin down how many more civil servants Whitehall may need.