The Labour peer said the Commons’ Public Accounts Committee should hold a probe with the equivalent Holyrood committee.

Speaking to The Scotsman, Lord McConnell, right, said: “This is about the fact that because the SNP were the third largest party at Westminster for the best part of 10 years, they received over that time millions of pounds of public money to organise their party affairs.

“Obviously, there are also issues about signing off accounts, and how seriously that was all taken, and I think on all these areas, there are issues to be looked at, and recommendations that must be made.

“So, I think this should be a joint public inquiry.”

The peer said a joint inquiry would help avoid accusations that Holyrood was presiding over a “cover-up” or that Westminster was carrying out a “hatchet job” on the SNP.

He said the investigation could examine the relationship between the Scottish Government and the Crown Office, and whether public funds provided to the SNP at Westminster were involved in the embezzlement.

Murrell pleaded guilty to embezzling £400,000 from the SNP at the High Court in Edinburgh last week.

Giving her first major interview since the guilty plea, former first minister Nicola Sturgeon – Murrell’s estranged wife – said she “rejected completely” the idea that figures within the party were attempting to raise concerns about the “behaviour that Peter pleaded guilty to on Monday”.

She said: “I will take responsibility for the things I do, the decisions I make. I’m sitting here with you right now, answering questions because I believe strongly in that accountability.

“But I am not responsible for the crimes that my former husband committed, and I’m not going to apologise for somebody else’s crimes.”