Ms Vermund, the leader of Nye Borgerlige or ‘The New Right’ party, wants Danes to be given a vote on their membership of the European Union.
Speaking exclusively to Express.co.uk, the anti-Brussels politician said if Mrs May is able to overcome EU bullying and secure a good Brexit deal, more people will see it is possible to exit the bloc.
Ms Vermund said: “I hope Danes will get a referendum. I think many Danes are closely watching what is happening with Brexit.
“If Theresa May, who I have great expectations for, can get good deals, I’m sure Danes will feel more secure in regards to a referendum on a membership we entered alongside Great Britain.”
EXPRESS • GETTY
Pernille Vermund said Theresa May could pave the way for Denmark to leave the EU
The right-wing Dane also criticised Brussels using “mafia-like methods” and risking a future relationship with Britain.
Ms Vermund added the EU’s treatment of Britain after it voted to leave in the June referendum was reason enough itself for others to flee the union.
She said: “I hope they don’t, but the way they are acting in the EU, it wouldn’t surprise me [if they punished the UK].
“For me, it is very obvious that if one becomes a member of something where you’ll be punished for leaving the fold, then you should just stay clear.
If Theresa May can get good deals, I’m sure Danes will feel more secure
“For me, the EU is almost using mafia-like methods.”
Ms Vermund also took the British in defence as she insisted it would backfire on Brussels if the bloc demands the UK pays the astronomical exit bill currently on the table.
“I think it is deeply unreasonable to demand Britain pays for something they are not participating in,” she said.
“I hope the negotiations can result in a good Brexit deal.
May meets Juncker and Barnier at Number 10
Wed, April 26, 2017
Theresa May hosted European Commission President Jean-Claude Juncker and chief negotiator Michel Barnier at Downing Street for the first face-to-face talks since she triggered the two-year process of withdrawing from the EU
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Prime Minister Theresa May greets European Commission President Jean-Claude Juncker ahead of a working dinner at 10 Downing Street, London
“We all need Great Britain to emerge as a rich and prosperous nation because we naturally want to continue trading with Great Britain, travel to Great Britain and allow British nationals into our countries because those British nationals have much to offer.”
Meanwhile, Danish MEP Anders Vistisen warned the bloc against hitting the self-destruct button by punishing the UK for leaving the union.
Mr Vistisen, of the Danish People's Party, argued a hard-line approach would result in Brussels driving away other members, as any punishment handed to the UK would affect Ireland too.
The Danish politician said: “In the European Parliament there is this sentiment of being angry, being disappointed in the British.
“But let’s be honest, the member states know that we are dependent on each other in security matters, and also in trade matters.
“From a Danish point of view, we would lose one of our biggest trading parties, same thing for Germany, same thing for the Netherlands and Belgium.
“Especially Ireland I think will be a moderating factor here because every time you punish Britain, you punish Ireland also.”