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

Speaking after the Sunday morning service at Crathie Kirk near her Balmoral estate in Scotland, the Queen told a well-wisher: "Well, I hope people will think very carefully about the future."

The remarks were interpreted by no campaigners as being helpful to their cause. British prime minister David Cameron will on Monday use his final visit to Scotland before the referendum to say that a yes vote will lead to a split "for ever".

The Queen made her remarks 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. But her remark was seen to tally with no campaigners claims that a vote for independence would lead to an irrevocable break with the UK.

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, which were first disclosed by the Times's Scottish political editor Lindsay McIntosh, 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. The prime minister will reinforce this point on Monday when he says: "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 rerun.

"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."

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."

It has been stressed that the speech in 1977 was made in different circumstances when there was no devolution legislation before parliament. A proposal to establish a Scottish assembly was narrowly passed in a referendum in 1979. But it ultimately failed because the yes vote was below 40% of the overall electorate.

Alex Salmond, the Scottish first minister, highlighted the significance of the monarchy when he moved on Sunday 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."