Mr Starmer said the Scottish government should abolish the dual role of the lord advocate who is both chief prosecutor and chief legal adviser to the Scottish government.

“This is a really important issue. Labour in Scotland have been really clear they would separate the roles, that is the right thing to do,” Sir Keir said in the Commons.

“It is the obvious thing to do, that is what we do in England and Wales.”

Mr Starmer added: “They really do need to bring forward proposals now to deal with the problems sitting there for a very long time.”

He was commenting in response to a question from Scottish Conservative MP John Cooper.

Mr Cooper asked: “Incredibly, in Scotland, we have a situation where the head of prosecutions the lord advocate does sit in the cabinet. This has been thrown into sharp focus lately by a police probe investigation into the finances of the SNP.

“It has further been thrown into sharp focus because ultimately… the lord advocate does ultimately sit at the head of the investigation into the former first minister Nicola Sturgeon who faced potential criminal charges.

“This situation has been created by the SNP, they will not fix it. Does it sit with this House to amend this situation?”

In a statement last week, a spokesperson for the Crown Office said that the lord advocate was not involved in the decision not to charge Ms Sturgeon or SNP treasurer Colin Beattie.

The statement said: “Professional prosecutors from COPFS and independent counsel are dealing with this case without involving the lord advocate or solicitor general. All Scotland’s prosecutors operate independently of political influence.”