The Queen made a rare intervention on the political stage when she expressed the hope that voters will "think very carefully about the future" before the Scottish independence referendum on Thursday.

As David Cameron prepares to issue a warning in Scotland that a vote for independence will lead to a permanent split from the UK, campaigners for the union welcomed the Queen's remarks as a reminder of the monumental decision facing voters in Scotland.

The comments by the Queen came as she left Crathie Kirk near her Balmoral estate in Aberdeenshire after the Sunday morning service. The Queen told a well-wisher: "Well, I hope people will think very carefully about the future."

The Queen's remarks were interpreted by no campaigners as helpful to their cause. They were seen to tally with a warning the prime minister will deliver in Scotland on Monday, on his final visit north of the border before Thursday's vote, that a vote for independence would lead to an irrevocable break with the UK.

The prime minister will say: "This is a once-and-for-all decision. If Scotland votes yes, the UK will split, and we will go our separate ways for ever."

Downing Street sources said that Cameron would also have a positive message about the benefits of remaining in the UK. He may refer to a decision by David Beckham to put his name to a long list of celebrities, actors and cultural figures who have signed an open letter urging Scotland to vote no. Organised by the TV historians Tom Holland and Dan Snow, their "stay with us" campaign is due to hold a vigil in Trafalgar Square, London, tonight.

A series of opinion polls confirmed the two campaigns are in effect neck and neck. An Opinium poll for the Observer found that no was six points ahead with 53% to 47% for yes. A further poll by Panelbase for the Sunday Times put the two campaigns only two points apart at 51% for no and 49% for yes. A further ICM poll for the Sunday Telegraph gave yes a more dramatic lead of 54% to 46%, but its significance was played down since its sample was only 700, under the normal threshold of 1,000 voters.

Alex Salmond said that the "extraordinary manifestations" of support he has encountered during a whistle-stop tour of Scottish towns and cities over the past 72 hours has convinced him he is on the verge of a historic victory that would lead to the collapse of the 307-year-old union.

Pointing to the Scottish National Party's shock landslide victory in the 2011 Holyrood elections, where it won the first overall majority since devolution in 1999, the first minister told the Guardian: "I sense a momentum which is much greater than that. I experienced that campaign and I knew what was happening – it was great but I see now on the streets of Scotland today – the east end of Glasgow and Dumfries where 500 people arrived out of nowhere to campaign on the bridge over the Nith – these are extraordinary manifestations of people mobilised because they sense the momentum for Scotland; this time of opportunity, this chance of a lifetime."

Salmond had earlier moved to reassure traditionalists when he said the "Queen and her successors" would remain as head of state in an independent Scotland. He told the Andrew Marr Show on BBC1: "We want to see Her Majesty the Queen as Queen of the Scots. That is a fantastic title and a fantastic prospect."

The Queen indicated that she is fully seized of the historic importance of the referendum when she spoke about the vote outside Crathie Kirk after a well-wisher joked that they would not mention the referendum. The Queen, who remains above the political fray as a constitutional monarch, observed the proprieties of not endorsing either side in the referendum.

A Buckingham Palace spokeswoman said: "We never comment on private exchanges or conversations. We just reiterate what the Queen has always said: she maintains her constitutional impartiality. As the Queen has always said, this is a matter for the people of Scotland."

But the Queen's remarks were warmly welcomed in private by the pro-UK side, who are keen to impress on voters that they will make an irrevocable decision if they vote for independence. In his address, the prime minister will say: "This is a decision that could break up our family of nations and rip Scotland from the rest of the UK. And we must be very clear. There's no going back from this. No re-run."

The remarks by the Queen came after the palace insisted last week that the monarch, who spends every summer at her Balmoral estate and whose mother was Scottish, was remaining above the fray in the referendum. This followed reports that the Queen was horrified by the prospect that her kingdom may be broken up.

Nigel Farage, the Ukip leader, weighed in last week when he said it "might be handy" if the Queen intervened on behalf of the pro-UK side. Some campaigners for the union have pointed out that in 1977, the year of her silver jubilee, the Queen said in a speech in Westminster Hall: "I cannot forget that I was crowned Queen of the United Kingdom of Great Britain and Northern Ireland."

Salmond insisted that a yes vote was thriving because of a "joyful, liberating and empowering" grassroots campaign. But the yes campaign came under heavy attack after hundreds of pro-independence protesters marched to the BBC Scotland headquarters in Glasgow calling the BBC's political editor, Nick Robinson, a "liar", and demanding he be sacked.

Robinson clashed with Salmond last week after the BBC journalist pressed the first minister over threats by banks to leave Scotland. The crowd accused the BBC of "killing democracy", claiming in one large banner that Robinson was "a totally corrupt journalist these days, typical of the British Biased Corporation".

Alastair Campbell, Tony Blair's former head of communications, tweeted: "had my run-ins with BBC, but organised protests like the one going on now is beyond Tebbit, and not far off Putin. Vote YES for intimidation". Further evidence about the deep misgivings of the UK's largest companies emerged after 78% of company chairmen in FTSE 100 companies said independence would damage the economy, according to a poll by the executive consultancy Korn Ferry. Only a third of the 28 chairmen polled said they were "fully prepared" for a yes vote.

The centre-right Centre for Policy Studies thinktank warned that Scotland faced a £14bn black hole in its budget, because of an expected slump in North Sea oil forecasts and "the probable flight of a large proportion of the financial services sector from Scotland."

• This article was amended on 15 September 2014. It mistakenly described Tom Holland as an actor. He is, among other things, a TV historian. This has been corrected.