The former Commons Speaker joined the Labour Party earlier this summer.
The proposed scheme would impose regulations in a bid to tackle the growth of rentals in areas such as Edinburgh.
Business Secretary Kwasi Kwarteng met with oil companies and retailers on Sunday to address the issue.
People will have to prove they have been double vaccinated before they can enter nightclubs or attend some other large events.
She reportedly described the Tories as 'scum' at a Labour party conference reception.
The temporary visa scheme will see opportunities created for 5000 HGV drivers and 5500 poultry workers.
The former leader took aim over plans to change the rules for future leadership elections.
Brian Wilson, who served as industry and energy minister in Tony Blair’s government, will lead the new body.
Worker shortages have been linked to both the coronavirus crisis and a lack of European labour after Brexit.
The case was made by Scottish Labour MSP Katy Clark.
Jenny Gilruth, Europe minister with the Scottish Government, raised her concerns about the move in a letter to Therese Coffey.
A total of 114 soldiers have been drafted in, with the first deployment of drivers expected to be behind the wheel from Sunday.
Transport secretary says Scottish Government 'reluctantly concluded' that alignment with the UK is 'the best option'.
Former Commons Speaker John Bercow defects to Labour
