"Ministers are increasingly nervous that a Scottish breakaway is on the cards (the cabinet was recently briefed that the latest opinion polls show 56% of Scots would vote for independence, and 44% to stay in the UK)."
James interprets that as meaning private polling is showing an average Yes vote of 56% - which of course would be slightly higher than the public polls have shown over the summer. However, there's no actual mention in the article of any private polls, and it could just be that the briefing was about the polls we already know about, and that the figures cited are slightly inaccurate.
That said, private polling does go on. Members of the YouGov panel are periodically asked about independence using a non-standard question, and the results rarely see the light of day, so that must be either private polling or for internal use.