But the SNP has said that if it wins a parliamentary majority at elections scheduled for May 6, it will pass its own bill so that a referendum can take place once the pandemic is over.
Scotland's Nicola Sturgeon has accused Boris Johnson of "fearing democracy".
In Scotland, the poll found 49 per cent backed independence compared with 44 per cent against - a margin of 52 per cent to 48 per cent if the undecideds are excluded.
The Prime Minister, who has made clear he does not support a second independence vote, said: "The whole United Kingdom is going through a pandemic, I think what the people of the United Kingdom want to see is everybody focusing on beating that pandemic, which we are, rolling out the vaccine, and getting ready to bounce back from that pandemic and have the strongest possible economic recovery". Ms. Sturgeon says her Scottish National Party will run in May's election "to seek the authority of the Scottish people" for a new referendum.
Scotland's First Minister Nicola Sturgeon said on Sunday that she will seek a referendum on independence if her Scottish National Party (SNP) wins elections in May, even if there is continued opposition from Westminster.
"And if they give me that authority that's what I intend to do".
Ms. Sturgeon argues that Brexit has transformed the situation by dragging Scotland out of the European Union against its will.
"The polls now show that a majority of people in Scotland now want independence".
In response to the SNP's "roadmap", the UK Government said the issue of Scottish independence was settled "decisively" in 2014. If Mr. Johnson's government refused to agree, the issue would likely end up in the courts.
The PM has pledged to refuse such a request.
Reporter Fatima Manji then asked Mr Russell: "The problem you got though is that the Westminster Government and Boris Johnson have been clear that they're not going to be granting the right for a referendum any time soon, what will you then do?"
UK Government sources said it would be more likely to ignore a referendum, although that would lead to huge political fallout.
Unless the United Kingdom is fundamentally reformed it could swiftly become a failed state as many people have lost faith in the way the country is governed by, and in the interests of, a London-centric elite, former Prime Minister Gordon Brown said.
"I believe the choice is now between a reformed state and a failed state", Brown wrote in the Daily Telegraph newspaper.
Mr Johnson has repeatedly stated his opposition to another referendum while a cabinet spokesman said the Scottish public wanted to see British politicians "working in partnership to focus on defeating coronavirus".
Instead, the Prime Minister highlighted the AstraZeneca coronavirus vaccine as being a prime example of the "strengths and advantages" of the United Kingdom.
Meanwhile, a poll commissioned by the Sunday Times in Northern Ireland found 51% of people wanted a referendum on Irish unity in the next five years.
In Northern Ireland, 47 per cent still want to remain in the UK, with 42 per cent in favour of a United Ireland and a significant proportion - 11 per cent - undecided.
In an interview with BBC Radio 4's Today, he said at a time "when all should be pulling together and intensifying co-operation across the UK" there was division and claims by the leaders of Scotland and Wales and the English regions that they were not being properly consulted.