Murphy said he “wanted to catch up privately about a couple of political issues” with the Tories.

However a Westminster source suggested Murphy, who was a Cabinet Office minister, Europe minister, and finally Scottish Secretary under New Labour, had offered the pair tips on high office.

The SNP last night called on Mundell to make a full disclosure about the talks, especially as Murphy now runs a one-man business advising foreign governments.

Murphy, 49, led Scottish Labour to its worst general election result last year, losing his own East Renfrewshire seat as 40 of the party's 41 constituencies fell to the SNP.

The collapse followed his highly divisive tour of Scotland for the Better Together campaign during the independence referendum.

Late last year, he set up a consultancy, Arden Strategies Ltd, and began working for Finland’s Crisis Management Initiative (CMI) advising on “conflict resolution in central Asia”.

He took part in a CMI meeting with government staff in Armenia in October, then popped up in Georgia, the pro-Western former Soviet state in the Caucasus, for a peace workshop with local officials.

Now material obtained by the Sunday Herald under Freedom of Information shows that Murphy also had meetings with a government rather closer to home.

In his own words, he had a “good conversation” with Mundell in December, then followed it up with a meeting with Dunlop at Dover House on Whitehall in February.

An email trail shows Murphy contacted Dunlop’s diary secretary on January 19.

He wrote: “Apologies for the impersonal approach and for getting in touch out of the blue, but I wanted to see if I could get a slot in Andrew’s diary at some point soon. I just wanted to catch up privately about a couple of political issues.

“I had a good conversation with David Mundell on similar terms before Christmas.”

A week later the secretary replied saying Dunlop was “happy to meet with you”, and offered a choice of 11 possible times and dates in February and March.

Barely an hour later, Murphy grabbed the first available slot, midday on February 17. “Should I come to Dover House?” he asked.

When the secretary confirmed the meeting, Murphy emailed his thanks and included a shameless link to a website selling his “acclaimed book” about football.

The Scotland Office said no notes were taken during Murphy’s half-hour meeting with Dunlop. Nor was any briefing material prepared for Dunlop.

An SNP spokeswoman said: “It seems Better Together is still alive – even if it isn’t very well."

A Scotland Office spokesman: “This was a meeting between a previous Scottish Secretary and a current Scottish minister to discuss Scottish issues. There is nothing surprising in that.”

Murphy failed to respond to calls and emails.