The Church of England has launched an investigation into the running of cathedrals, as financial crises threaten the future of some of the country’s most cherished buildings.

As Christians prepare to mark Holy Week and celebrate Easter Sunday, Anglican leaders have become increasingly concerned about reports of staff sacked, heavy debts accumulated and assets sold off.

On Monday the church will announce the 12 members of a working party ordered by the archbishops of Canterbury and York, Justin Welby and John Sentamu, to look into the way cathedrals are governed, their accountability and how financial decisions are made. The working party will include financial specialists and other experts and will be chaired by the bishop of Stepney, Adrian Newman, with the dean of York, the Very Rev Vivienne Faull, as deputy chair.

The inquiry has been prompted by a recent report into the financial problems at Peterborough cathedral, where difficulties had led to the departure of the dean and the risk that the church might be unable to pay staff their salaries. A loan from the Church Commissioners helped deal with the immediate shortfall for the 12th-century former Benedictine abbey, housing Catherine of Aragon’s tomb, but 12 staff were made redundant.

The report into Peterborough by its bishop, Donald Allister, warned that the position was so grave that it showed the governance framework for Anglican cathedrals, which allows them to be independent, could cause “serious risks to the reputation of the whole church”. He said Peterborough had complied with the 1999 Cathedrals Measure, which governs their running, but the scrutiny and safeguards in the regulations were “clearly insufficient to prevent the problems that occurred”.

Guildford cathedral. Plans to develop houses on surplus land have failed. Photograph: Loop Images/UIG via Getty Images

Peterborough is not alone. Among other cathedrals facing difficulties are:

■ Exeter, where the dean has been accused of poor financial management by the bishop, the Rt Rev Robert Atwell. There has been talk of staff redundancies and the cathedral faces a predicted deficit of £175,000 after a failed £8.7m plan to restore the Roman baths on the site.

■ Guildford, Surrey, where plans to build houses on surplus church land that would have raised a £10m fund have been thrown out by the council. The cathedral is losing £100,000 a year.

■ Durham, which has an annual deficit of £500,000. Its annual report says it faces “continued pressure on traditional revenues (rents, income, dividends)”. Income from “newer commercial activities is increasing, but not at a fast enough rate to cover our running costs”.

■ Ripon, which is running a deficit of £40,000 on income of £1.34m, though it has cut the deficit from £250,000 five years ago.

Under the Cathedrals Measure, which will be under scrutiny by the working party, each cathedral is run independently by a dean and chapter, while it is also governed by a council of lay people which meets twice a year to advise the chapter and a college of canons. Both of the latter can see the accounts. The local bishop acts as a regulator. According to Newman, the working party chairman: “It is time to look at these measures again and ask whether they are fit for purpose. The buildings themselves are a huge problem. It is possible to see a cathedral as an albatross, but they are also our best assets. But cathedral ministry is challenging and this has become more acute.”

The crisis for cathedrals comes at a time of great success. The most recent statistics, for 2015, show attendance for worship continues to grow, with midweek services the main cause of the increase. On average, 36,700 people attended each week in 2015, with Christmas attracting 125,200 worshippers. The second most popular day was Easter Sunday, with 54,000 going to a cathedral service. Meanwhile, the Association of English Cathedrals estimates that cathedral tourism generates £91m and supports 2,800 jobs. York Minster alone gets 490,000 visitors a year.

But the biggest headache for deans is the huge cost of repairs. The finances are complicated. The bulk of their income has to be raised by the churches themselves, although the Church Commissioners award £9m a year towards stipends and pensions.

Other money comes from legacies, donations, selling off assets, grants from the Heritage Lottery Fund and entrance fees, though only nine of the 42 English cathedrals charge them. The dean of Wells, the Very Rev Dr John Davies, said his cathedral was against entry fees. Instead it relies on bequests and film location fees. “We have 250,000 tourists a year,” he said, “but we would not countenance a fee. It seems wrong.”

Exeter cathedral is expecting to report a £175,000 deficit. Photograph: Olaf Protze/LightRocket via Getty Images

In spite of its financial problems, Durham cathedral is also against entry fees. The 12th-century church is investing in visitor attractions in adjoining buildings, for which it will charge admission prices. Paul Chandler, chair of its council, said: “Unlike some other cathedrals we also have assets we can make use of – we can sell off agricultural land for development and we have historic objects we can loan at a fee. But we must also trim costs. We do not have a particular plan for redundancies but we can’t keep adding staff.”

Other cathedrals have opted for very secular money-raising ventures, such as hiring out their naves for corporate dinners and fashion shows. At Peterborough, the nave will be used next month for Strictly Cathedral, a £25-a-head dance show and prosecco reception starring the Olympic gymnast and Strictly Come Dancing champion Louis Smith.

A further recent boost came from the First World War Centenary Cathedrals Repair Fund, set up by former chancellor George Osborne, which provided £40m over two years for repairs. The dean of Ripon, the Very Rev John Dobson, said that the fund had enabled his cathedral to carry out repairs that should have been done 20 years earlier. Faull, the working party vice-chair, said deans would be lobbying the government for a fund similar to Osborne’s.

“The first world war fund was a godsend,” she said. “Major building works and urgent repairs are the shocks that can cause the financial problems, especially for the smaller cathedrals.”

The Archbishops’ Council, headed by Welby and Sentamu, wants the working party report finished by December. But the focus on finance does not please everyone. The dean of Peterborough, the Very Rev Charles Taylor, warned in his final sermon that deans and bishops are sent on courses “not to hone their skills in theology, or liturgy, community outreach or pastoral care, but to take a mini-MBA. The pattern of the Good Shepherd has been hijacked by the model of the chief executive officer.”

• This article was amended on 9 April 2017 to correct the main image. An earlier picture showed St Albans Cathedral rather than the one in Peterborough.