Speaking on Newstalk’s The Hard Shoulder, Brolly – who has been critical of the party in the past – said: “I’ve been making this point for a long time – the DUP is a cult.
“It was created in the image of Ian Paisley and it was one man’s… outlook on the world. I mean, a brilliant communicator. So charismatic.
“But like all cults, sooner or later, a cult self-destructs because by definition it doesn’t adapt to a changing world and that’s what we’re seeing with the DUP.
“They’re trapped in this fantasy of ‘Never, never, never’ and ‘Ulster is British’ and all of that… and it’s just fallen apart”.
Poots resigned following Paul Givan and Michelle O’Neill being officially appointed as Northern Ireland’s First and Deputy First Ministers.
Poots formally nominated Lagan Valley MLA Paul Givan as Northern Ireland’s new First Minister at a special sitting of the Stormont Assembly.
Sinn Fein’s Conor Murphy also nominated party colleague Michelle O’Neill as Deputy First Minister at the same special sitting.
However, it is understood that 20 DUP MLAs voted against the decision to nominate Givan, but that Poots went ahead with the nomination, provoking a backlash from the party.
It comes as the British government agreed that it will introduce an Irish language act in Northern Ireland in October if the Stormont Assembly does not do so by September.
Speaking about Poots, Brolly said: “Edwin agrees to an Irish Language Act, which after all was agreed in 2006 in order to get Stormont up and running and he’s mercilessly deposed – and, I mean, Edwin would be seen as the old-style evangelical embodiment of the DUP.
“So, you can see that there’s very little room for manoeuvre here, and what you’re seeing is the death spiral of the DUP”.
Brolly told the programme it is hard for him to see how the DUP can occupy “any modern space in politics”.
He said: “When Ian Paisley said ‘Never, never, never’ and ‘We’ll spill blood to keep Ulster British’… it was in the middle of the Troubles.
“But the Troubles are gone – the North is the most peaceful country, in terms of domestic crime, in western Europe.”
On the party’s future, he added: “Therefore I think what will happen inevitably is that it will split into the hardline evangelical party that it is at its core traditionally and then the other side of it is going to have to decide ‘Well look, do we run with the party simply to get votes?'”
You can listen to the full conversation with Brolly here.