Cabinet ministers are being told that some of their most prized projects cannot be developed because so many officials have been diverted to delivering Brexit, it has emerged.

Ministers’ priority programmes have fallen victim to “re-prioritisation”, according to internal government warnings seen by the Observer.

Government insiders said they knew of examples of officials usually dealing with schools and hospitals who were now redeployed to work on farming and fishing as a result of the scramble to prepare for all Brexit outcomes, including no deal. “It’s a real worry now that things are being held up and not happening,” said one senior Whitehall source. “We are really starting to see it as the Brexit process drags on and on.”

A memo to a senior minister, said: “In the context of ongoing cross-government re-prioritisation exercises, departments have not yet been able to resource the necessary cross-government team to deliver the work.”

The government’s plans for resolving the crisis in social care and a review of university finance are among the major policy proposals that are said to have been held up by Brexit, while many other areas have suffered due to the lack of parliamentary time and political instability.

It’s a real worry now that things are being held up and not happening Senior Whitehall source

With Britain’s EU exit looming, no-deal planning is also causing tensions in cabinet as senior ministers are forced to finalise the measures they will take to avoid economic collapse. Several sources across Whitehall said that the Treasury was trying to secure ways of protecting the economy in a no-deal outcome, including the use of zero tariffs on some imports in order to combat inflation. However, the Department for Environment, Food and Rural Affairs has demanded greater protection for British farmers in a no-deal Brexit, by placing higher tariffs on imported produce.

Intense discussions have been taking place over the last week, with ministers having to finalise their plans before the end of the month. It means key decisions over no-deal planning are being taken with just over a month to go until Britain is due to leave the EU.

The sheer size of the task has seen the civil service expand every year since the 2016 referendum, but there are now clear signs that other policy areas are suffering as a result.

Less than a fifth of the 133 major projects being developed are likely be delivered on time and on budget, according to the Institute for Government thinktank. Some, including the HS2 rail line, are rated as “amber/red” – meaning there are “major risks or issues apparent in a number of key areas”.

Delays to social care plans are causing acute concerns within local government and the NHS. The charity Age UK has warned that more than 50,000 people have died waiting for care due to delayed ministerial plans.

The private sector is also warning of Brexit inertia. The construction company Galliford Try said last week that companies are not investing because of political indecision. It said no-deal would cause “a potential severe decline in consumer confidence and economic activity in general”.

John Manzoni, the civil service’s chief executive, recently admitted the government could not be fully prepared for a no-deal Brexit. He said it would inevitably lead to a “bumpy” departure.