The British and Irish governments have expressed the view that the time is not right for a border poll to be held, especially as tensions remain over the policy regarding the flying of the Union flag.
But Sinn Féin have continued to campaign for the public to get to vote on the future of Northern Ireland and whether or not it should remain part of the United Kingdom.
The DUP, who have suggested "calling their bluff" on the issue, made David Cameron aware of the findings of a BBC Spotlight survey during Prime Minister's Questions on Wednesday.
"I sometimes try and avoid opinion polls, so I haven't seen that one," Mr Cameron told DUP Lagan Valley MP Jeffrey Donaldson and the House of Commons.
"But it looks like one that will lift the spirits of almost everyone in this House, because we believe in a United Kingdom and we believe in Northern Ireland being part of that United Kingdom."
Among the survey's findings, more than 90% of respondents who identified themselves as Protestant wanted Northern Ireland to remain part of the UK.
Of those who identified themselves as Catholic, 38% also backed the Union - three percentage points more than backed a united Ireland.
When it came to the Union flag at Belfast City Hall, an overall 35% supported flying it 365 days a year - compared with 44% who supported the 18 designated days policy and 10% who thought it should not be flown at all.
The BBC said the poll was carried out by Ipsos Mori researchers, who interviewed more than 1,000 adults at 64 locations in Northern Ireland last month.