The scale of the government’s reliance on management consultants has been laid bare as analysis shows that spending with eight top firms has risen by 45% to more than £450m in three years.

Deloitte, the professional services firm, was the biggest winner, earning fees of £147m from public funds in 2019-20, compared with £40m two years earlier, amid a bonanza related in large part to Brexit.

The Home Office had the biggest increase in consultancy spending over three years, jumping 788% to £57m as the department dealt with security, immigration and border preparations for leaving the EU.

The results of the analysis of more than 11,000 government invoices came on Tuesday as Boris Johnson promoted the private sector, saying “free enterprise” must lead the recovery from the coronavirus pandemic.

In his speech to Conservative party conference, the prime minister sounded a warning about the extent of state intervention on schemes such as furlough and said: “There comes a moment when the state must stand back and let the private sector get on with it. We must not draw the wrong economic conclusion from this crisis.”

However, last week the minister in charge of curbing Whitehall spending, Theodore Agnew, wrote a letter to senior civil servants saying the civil service had become “infantilised” by an “unacceptable” reliance on expensive management consultants.

While 1% of civil servants are paid more than £80,000 a year, day rates for management consultants working in the public sector range from about £1,000 for junior consultants to about £3,500 for partners.

Research carried out by the data provider Tussell has identified how much each of the government’s ministries has spent with eight consultancies between 2017-18 and 2019-20.

The highest-spending department on consultancies in the last financial year was the Department for Transport, which has paid out £88m, a three-year increase of 156%.

The Cabinet Office, the department from which Lord Agnew and his close political ally Michael Gove oversee civil service expenditure, has nearly trebled its spending on outside consultancies over three years to reach £37m, the analysis showed.

The Department for International Development spent £67m on management consultancies in 2019-20 while the Ministry of Defence, which has been criticised in the past for its reliance on contractors, cut expenditure on consultancies from £93m in 2017-18 to £58m this year.

Deloitte appears to be the preferred consultants for the Home Office, having received £73m out of £110m spent on external advisers since 2017-18. Although many of the Home Office contracts are related to Brexit, the biggest Deloitte contract with the department is £60m, spent on the Emergency Services Network.

PricewaterhouseCoopers was the second biggest-earning consultancy from the public purse last year, receiving £106m, according to the analysis. It has earned a total of £294m over three years. The data shows that PwC was paid £32m by the Cabinet Office over three years out of a total departmental spend on the eight consultancies of £121m.

Over that period, PwC has recruited key figures who know the Cabinet Office well, including Gavin Barwell, Theresa May’s former chief of staff, and Philip Rycroft, the former permanent secretary who held senior positions across Whitehall.

The Ministry of Defence appears to have a close relationship with KPMG, having paid the firm £76m out of a total consultancy spend of £203m between April 2017 and March 2020.

Several senior figures have left the MoD to become paid advisers to KPMG, including Air Marshal Sir Simon Bollom who left his job as chief of materiel (air) in defence equipment and support in 2016 and soon after advised the management consultancy on RAF Brize Norton. He has now returned to the MoD as the chief executive of defence equipment and support.

Over the last year, EY earned fees across Whitehall worth £75m, while KPMG was paid £57m from government departments, according to the analysis.

The other four major consultancies – PA Consulting, McKinsey, BCG and Bain & Co – signed deals worth a total of £76m last year, the analysis showed.

Management consultants are typically brought in where it is thought specialist advice or expertise is needed, but there have been longstanding concerns over the extent of their use in the public sector.

Many senior civil servants or ministers work for consultancy firms at some stage in their career, so there are often strong personal links or relationships between staff on both sides.

Cabinet Office data reported by the National Audit Office last year showed a significant drop in spending on consultants after the introduction of new controls in 2010, from almost £2bn in 2009-10 to £400m-£700m in each of the following six years.

A spokesperson for Deloitte said: “We are confident that our work adds significant value to the public sector organisations we work with.

“Deloitte works closely with the Home Office, its agencies and police forces, assisting on their largest and most complex programmes and building and delivering new technologies.”

A PwC spokesperson said the firm follows all relevant rules and regulations when employing former politicians and civil servants. “We are brought in to provide specialist skills at speed where the breadth and depth of our experience makes a positive difference. We work alongside public sector clients to help tackle complex problems and situations where our expertise is needed,” he said.

A government spokesperson said they did not recognise some of the figures in the analysis. “We continue to take considerable steps to reduce unnecessary spending and protect taxpayers’ money,” they said.

“Ministers are concerned that the government is too reliant on consultants and have written to departments to make clear that services should only be procured when external expertise is essential and represents value for money. Where possible, we want to harness the wide range of skills within the civil service.”

KPMG declined to comment. EY has been approached for comment.