Britain’s four biggest accountancy companies are facing fresh scrutiny, with the head of the industry watchdog calling for the competition regulator to investigate their auditing activities following the collapse of Carillion.

Stephen Haddrill, the chief executive of the Financial Reporting Council (FRC), told MPs at a joint select committee hearing on Tuesday that “there should be more competition in the major accounting and audit area”.

Haddrill said he would ask the Competition and Markets Authority to look at the sector again. In 2013, its predecessor, the Competition Commission, criticised the big four for their close relationships with chief executives.

He was responding to Frank Field, the Labour MP and chair of the work and pensions select committee, who asked whether KPMG, Deloitte, EY and PricewaterhouseCoopers should be broken up. It is conducting a joint enquiry with the business committee into Carillion’s collapse.

Field noted that two of the construction company’s recent finance directors had previously worked for KPMG and it had audited Carillion’s accounts for the past 19 years. “They are all mates, aren’t they?” he said.

The FRC has opened an investigation into KPMG’s auditing of Carillion’s accounts in recent years. The watchdog started closely monitoring the infrastructure company after it issued a surprise profit warning in July, Haddrill told MPs, but was unable to disclose this publicly because of confidentiality requirements. He agreed those rules needed to be reviewed.

“There must be enormous cause for concern about the way the company was governed. We all look at what’s happened with a degree of incredulity, so we need to look on what basis the directors were making those decisions,” he said.

Haddrill rejected MPs’ suggestions that the accounting watchdog was “toothless” but agreed that it needed more enforcement powers.

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It also emerged that Carillion is unlikely to have “enough assets to meet even the cost of winding up the company”, according to Sarah Albon, the chief executive of the Insolvency Service. The group collapsed with £29m in the bank, a £1.3bn debt pile and a pension deficit of close to £1bn.

Albon told MPs that Carillion was made up of 326 companies, 199 of them in the UK, with 169 directors. She said the Insolvency Service’s investigations normally took 21 months and it was putting “considerable resource” into the Carillion inquiry.

“One significant constraint is the incredibly poor standard of the company’s own record-keeping. It took some hours to identify how many directors we could potentially be targeting,” Albon said.

MPs heard Carillion borrowed to continue to pay dividends, but cited cashflow problems when pension scheme trustees pushed it for higher contributions. According to a parliamentary briefing released last week, it paid out £217m more in dividends than it generated in cash between 2012 and 2016.

Robin Ellison, the chair of trustees of the Carillion defined benefit pension scheme, insisted they had been “as tough as we could be. We weren’t just sitting there playing patsy with the company”.

He noted that the Pensions Regulator, which had had regular meetings with Carillion since 2008, could ask the company to make additional pension payments. “It would have been nice if they’d compelled the company to pay an additional £10m-15m contributions per year,” Ellison said.

He told MPs he was called into a meeting with the Carillion board the day before the company went into compulsory liquidation. “They felt if they could get over the cashflow issue, by the end of the month they would have refinanced the company,” Ellison said.

“I believe that they believed that they had a plan for the survival of the company which was manageable. In the end it wasn’t.”