Ian Paisley, a former MP for North Antrim, also emphasised his British identity as he took part in new podcast series Borderland by BBC Northern Ireland.
He is the son of Ian Paisley, one of the founders of the DUP who went on to serve as First Minister of Northern Ireland and later became Lord Bannside.
“It’s who and what I am. I’m a Brit, I’m a British citizen, I’m a British person, my identity is British, my history is British and my emotions are British,” he said.
He indicated to the podcast that he appeared on alongside former Sinn Fein MP Michelle Gildernew in at times testy exchanges that he was open to “persuasive arguments”.
“My mind is open, I’m a true believer in Britain and this place being British,” he said.
“But if you have got persuasive arguments please present them because to date I have not heard them.”
However, Mr Paisley also said: “My flag won’t fly in that country, the flag my wife’s great-grandfather perished for, and that’s a multi-generation thing.
“We have people who are living today who carry the bullet wounds for defending this country, their flag will not fly in that country, their sovereign will not be sovereign of that country.”
He also called for champions within the UK Government “who are prepared to recognise that Northern Ireland is an integral and essential part of the union”.
“I insist that a Cabinet and the Government has to make the case for the United Kingdom, otherwise why are they in this game?” he said.
In a statement on Tuesday, the DUP said they wished to “make clear that Mr Ian Paisley is appearing in this series in his own personal capacity and not on behalf of the Democratic Unionist Party”.
“As Ian is no longer in public office, he is entitled to give his own views but he is not appearing on behalf of the party,” they said.
“The Democratic Unionist Party is not interested in engaging or being persuaded on the so-called merits of a united Ireland or new Ireland or any other label those who want to pursue that aspiration might put on their latest project.
“We believe in the union and we are not open to taking part in discussions about a new Ireland and we will not be enticed by honeyed words designed to convey an impression that unionists would be welcomed and openly accommodated in a united Ireland.”
They went on: “A cursory examination of how unionists are treated when they find themselves in a minority tells us all we need to know and gives the lie to the narrative being pursued.
“Nationalists are trying to convince us that a united Ireland is inevitable.
“That is total rubbish. Leo Varadkar, whilst active in politics, did more to harm relationships between the Republic of Ireland and unionists in Northern Ireland than many of his predecessors and should learn from his mistakes rather than stirring up a divisive debate about a border poll.
“For us, we will promote the benefits of the United Kingdom and will not be diverted down the route of talking about any new Ireland or a divisive border poll that takes the focus away from the important ongoing real issues that people face on a daily basis.”
