Two-thirds of Britain's most senior civil servants are so demoralised that they are considering leaving their jobs, according to the first survey of mandarins to be conducted since the coalition's reform plans were published.

The poll (pdf), conducted by the FDA union (formerly known as the First Division Association) also found that almost one in four Whitehall staff in the top three grades of the service want to leave their jobs immediately. Many blame ministers' public criticisms of civil servants and a widening pay gap with the private sector as reasons for looking to move on. Others say there is an urgent need for structural pay reforms and a change to an institutionalised long hours culture.

The findings appear to confirm recent fears of a growing crisis within Whitehall since the coalition announced wholesale changes in June. Tensions have led to claims of a "cold war" between officials and ministers. They have continued to blame each other for a series of high profile mistakes including the West Coast mainline fiasco, the "omnishambles" budget, immigration rows, the mishandling of ash dieback and the bungled badger cull.

They follow a number of high profile resignations of permanent secretaries and anger over the way that Theresa May forced Brodie Clark, the former head of the border force, from his job in 2011.

According to Dave Penman, the FDA's general secretary, the survey shows that the government is facing "an exodus of talent" from the public to the private sector if the economy picks up.

"The members who responded are Britain's most senior public officials. If they are talking about this level of dissatisfaction, and pay in the private sector continues to rise while public sector pay is frozen, the government is at serious risk of losing people it cannot replace.

"The jobs that these people do are highly specialised and in some cases carry much responsibility – some are managing tens of thousands of staff. How will ministers replace such specialised people if they are criticising senior civil servants and public sector pay remains static?" he said.

Around 1,800 FDA members who make up round half of Britain's 3,500 deputy directors, directors and director generals within the civil service, were sent the survey in October. Of those, 506 responded.

More than 66% have considered leaving their jobs over the last 12 months, the survey found; 63% are more inclined to look for a job outside the civil service than they were 12 months ago; 24% want to leave their jobs as soon as possible. More than a third took no annual leave last year; 95% worked longer hours than they are contracted for; and over 70% say morale has plummeted over the last year.

Many civil servants said the service has been "publicly denigrated" by ministers and others, according to the union.

One member wrote: "It is the clear message given by ministers that the civil service is a waste of time, money and space. It is hard to take pride in a job that is not valued.

Another said: "I am fed up being criticised in public and described as a fat cat with no one defending me from the ministerial cadre."

In 2011, David Cameron described civil servants as "enemies of enterprise" and has privately described the comedy Yes Minister as a documentary.

Other ministers who have joined in the criticism include the education secretary, Michael Gove, who has told friends civil servants have blocked policy initiatives, the communities secretary, Eric Pickles and the minister in charge of the civil service, Francis Maude.

Labour began a pay freeze for senior civil servants in 2009 which has continued under the coalition. The government has set out a pay policy of a 1% increase a year for two years.

An independent review body has been assessing the pay of senior civil servants and is expected to report back in February or March.

The union has asked the review body to look again at senior civil service pay, which would examine the long term structural problems in the pay system including lack of progression, overlap of pay ranges, the role of performance-related pay and the relative position of pay levels.

Bernard Jenkin, the chair of the public administration select committee (PASC) which has launched an inquiry into the civil service, said that the results appeared to show that frozen pay and ministerial criticisms of civil servants may have damaged morale. "I am not surprised by these findings. Problems with morale have been suspected and we are exploring these issues in the PASC inquiry into the civil service. I have continued to question the wisdom of ministers publicly criticising their civil servants because it undermines trust in their leadership," he said.

A government source said that ministers are sensitive to changes in morale in the civil service and confident they will not lose their most valued staff as and when the economy improves. "There is a new generation of civil servants who are embracing change. The civil service is 15% smaller than in was in 2010. They are being asked to do demanding things and rising to that challenge. Is it all smooth? No. But through the reform programme, we hope it is changing for the better," the source said.

A Cabinet Office spokesman said the civil service continued to attract the brightest talent, despite the union's survey. "Our 2012 People Survey, which listened to the views of over 300,000 civil servants, shows that despite the difficult economic backdrop morale has held up, with an overall engagement score 58%, up two percent from last year and on a par with 2009, while the percentage who find their work interesting is at 89%," he said.