She has also denied there were factions of Labour MSPs and MPs within the party, insisting they were “joined at the hip” in doing the best they could.

She said that it was natural for there to “always be” a debate between MPs and MSPs, but she denied there had been the levels of interference stated by Ms Lamont.

After standing down, Ms Lamont accused the UK Labour Party of treating Scotland like a “branch office”.

Ms Baillie said: “Whether you are an MP or MSP in Scotland you are representing constituents in Scotland.

“It doesn’t matter what chamber you are in, you are absolutely joined at the hip in wanting the best that we can.” Ms Baillie has ruled herself out of the contest, saying she would rather play a “supporting role” than be leader.

She added: “I believe we should have a very open contest and I look forward to a number of different names emerging, be they MPs, MSPs or indeed MEPs, who are entitled to stand as well.

“But I think it would be really helpful to have a debate in the party where we have quite a lengthy nominations process that tries to balance a speedy transition, but yet a clear desire for the members to have their voice heard.

“I think you will see a number of people coming forward in the coming days and I look forward to that very much.” She added that she was disappointed the party would be using the electoral college method instead of one-member-one-vote.

The Labour Party is moving to a more straightforward way of electing its leaders but this contest will use the long-established collegiate system.

Nominations for candidates will open on Friday October 31, and close on Tuesday November 4.

The ballot will start on Monday 17 November, and the new leader will be announced on Saturday 13 December.