Speaking at the annual event, Mr Hunt warned that if the EU keeps member states prisoners much like the Soviet Union, it will only escalate the further disbandment of the bloc.
He said: “What happened to the confidence and ideals of the European dream?
“The EU was set up to protect freedom. It was the Soviet Union that stopped people leaving.
“The lesson from history is clear: if you turn the EU club into a prison, the desire to get out won’t diminish, it will grow – and we won’t be the only prisoner that will want to escape.”
Mrs May nevertheless rejected Mr Hunt’s comments when questioned on BBC1’s Breakfast show, stating firmly that the EU and the Soviet Union are “not the same”.
She said: “As I sit around that table in the EU there are countries there who used to be part of the Soviet Union.
“They are now democratic countries and I can tell you that the two organisations are not the same.”
However, the Prime Minister defended Mr Hunt’s statements in relation to Brexit, and urged the EU to respect the democratic will of the British voters.
She said: “I think the point he was making was an important one; it was that we had the biggest democratic exercise in this country’s history, it was the referendum vote in 2016.
“We should be respectful of delivering on that vote and across the EU it is important for people to recognise that vote and the need to deliver on that – that was the point he was making.”
Mr Hunt also defended his remarks and stated he was calling on the bloc to respect core European values of self-determination and liberty.
Speaking on CNBC, he said: “Any sensible reading of the speech would see that this was a passionate request and desire for friendship with our European neighbours going forward.
“But what I was saying was if the attitude of the EU is that someone who wants to leave the club has to be punished, then that’s not consistent with European ideals.
“The EU was partly set up to stand firm against Soviet totalitarianism, and I was just pointing out the contradiction that that’s what we were set up to stop.”
He called on the EU to change its attitude in regards to the Brexit negotiations, and urged them not to “tear up” the friendship which has built up between the UK and the EU over the last 20 years.
He said: “They need to sit down and they need to say that over the last 10 or 20 years, what’s mattered for Europe is that strong partnership between the UK and continental Europe, that’s what has given us peace and prosperity.”
The Foreign Secretary’s comments drew sharp criticism from his European counterparts, with Jean-Claude Juncker’s deputy Frans Timmermans accusing him of “insulting” EU member states which were formerly part of the USSR.
Manfred Weber, leader of the European People’s Party in the European Parliament, also said: “Now we experience a new level of populism when the Foreign Minister of Great Britain, Hunt, is comparing the EU to the Soviet Union.”
In a sharp warning, he said: “Mr Hunt, you should apologise for what you said.”