The latest data shows that the furlough scheme has cost the government £35.4bn so far. This means that between £1.75bn and £3.5bn could potentially have been paid out incorrectly.

Under the furlough scheme, employers can keep employees on the payroll even if they can’t work because of coronavirus. The government paid 80% of wages, up to a monthly maximum of £2,500, from March to September. It now pays 70% of wages up to a monthly limit of £2,187.50, with the scheme due to end next month.

HMRC’s permanent secretary Jim Harra told MPs on the public accounts committee that HMRC had made an assumption that the error and fraud rate in the scheme could be between 5% and 10%.

Both HM Treasury and HMRC were called to appear in front of MPs to explain how they were intending to reduce the problem.

Harra said: “What we have said in our risk assessment is we are not going to set out to try to find employers who have made legitimate mistakes in compiling their claims, because this is obviously something new that everybody had to get to grips with in a very difficult time.

“Although we will expect employers to check their claims and repay any excess amount, what we will be focusing on is tackling abuse and fraud.”

Harra advised that any worker who thinks their employer may have been fraudulently claiming furlough money can report it to the HMRC.

It was reported last month that about 3,000 companies were being investigated for furlough fraud by HMRC. The news came after several national newspapers ran stories claiming that six million workers broke the rules by doing their jobs from home during lockdown.

About 8,000 calls have been made to the HMRC’s fraud telephone hotline with the tax man investigating 27,000 “high risk” cases where they believe a serious error has been made.

Tax and advisory firm Blick Rothenberg says the missing £3.5bn may be just the tip of the iceberg.

Fiona Fernie, a disputes resolution partner at Blick Rothenberg, said: “This figure is purely an estimate and has been issued just a couple of weeks after HMRC issued the first 3,000 letters to firms asking them to check the amounts that they had claimed and warning them that they were under investigation.

“With many more businesses already under review with a view to investigation, it remains to be seen whether the estimate is accurate.  Only once the investigation programme is fully under way will it be possible to assess whether the problem is greater than currently anticipated.”