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This is a rush transcript from "On the Record," June 24, 2016. This copy may not be in its final form and may be updated.

GRETA VAN SUSTEREN, FOX NEWS HOST: Now, this message of frustration with the establishment parallels both Senator Bernie Sanders and Donald Trump's race for the White House.

Former Speaker of the House, Newt Gingrich, goes "On the Record."

Good evening, sir. And one of the things you tweeted today about this whole Brexit and about Donald Trump was this, "Solid, positive statement by real Donald Trump," that's his handle on Twitter, "on reaffirming U.S.- British ties after the Brexit vote. Churchill and Thatcher would be proud." What did you mean?

NEWT GINGRICH, FORMER SPEAKER OF THE HOUSE: Well, historically we have been very, very close to Great Britain, less close under Obama. His intervention was totally inappropriate. And he, sort of, threatened the British people. It back fired on him.

I think what Trump is saying is that first of all, he respects the British people's right to choose. And I think he would have been positive whichever way they went.

But, in addition, he wanted to reassure them that the unique relationship we've had with the Great Britain for a very long time will continue in a Trump Administration. I think that's something that Churchill, who worked very hard to foster the relationship and Thatcher who was extraordinarily close to Ronald Reagan, they would both have appreciated an American making that kind of statement.

SUSTEREN: All right. And would they not expect to hear that from other candidates? Would they expect to hear that from Secretary Clinton? Are you suggesting they would not?

GINGRICH: I think Secretary Clinton is so totally in favor of bureaucrats that she would automatically be in favor of Brussels over London. She is so in favor of large, complex, multinational operations that she would favor the European Union over Great Britain, just as she favors large, multinational operations over the United States.

The fact is you have the clear choice here. Do we move towards reform and towards taking back control of our country or do we continue to allow lawyers and diplomats and bureaucrats to set the path for us? And I think it's going to play out here as it has in Europe.

We just saw, by the way, two women elected as mayors of Rome and turn in a remarkable national uprising in which a comedian established a brand new anti-corruption party. They beat all the regular establishment parties. So the indicates that we're getting aren't just Brexit, but you're seeing again and again around the world, people are sick of their elites. They're sick of the corruption and they're sick of being told they have to obey some weird set of ideologies they don't believe in.

SUSTEREN: All right, let me bring the viewers in for a second. I'd like to bring them in to vote.

So viewers, now is your chance to vote at home on Twitter. Is Brexit good for Trump? Tweet yes or no, #greta. And we'll show live Twitter votes throughout the show.

Mr. Speaker, you mentioned the elites, in fact, you even tweeted about it that you said, "People are sick and tired of the elites and London dictating them. Populist insurgency very similar to the U.S.," tell me.

GINGRICH: Well, I think it's obvious. You had the entire British establishment who was opposed to leaving. From the Prime Minister on down, the financial leadership, the intellectual leadership, all of them said, "Don't leave, don't leave, don't leave." And the average voters ran over them.

You had the same thing happen in Rome and in Turin this week. You almost had it in Austria a couple of weeks ago for president. The insurgent barely lost. And the traditional parties are literally were not in the runoff because people are so sick of them.

I think this is a very strong signal that the election this fall could literally be the American people versus the Washington bureaucrats. And I think that bodes very, very badly for Hillary Clinton.

SUSTEREN: Is it because in your view both in Britain and United States is that the American people and the British people are so fed up with what the politicians are telling them, fed up with in fact the recession, fed up with the infrastructure falling apart, fed up with at least here with our tax system that that's not be (inaudible)? Is this just sort of another way to say enough and we want to move on and that we're sick and tired of the so-called politician elites telling us what's good for us?

GINGRICH: Sean Spicer of the Republican National Committee has this great chart that just has the word "enough." And the age of the -- is Hillary's age but with a downward arrow.

Yeah, enough of being told that Orlando was not about terrorism. Enough of being told that we have to pretend terrible schools have to be protected because the teacher's union wants them. Enough of being told that we have to allow in thousands and thousands of additional Syrian refugees about whom we know nothing and cannot possibly vet.

I mean, this go down the list of all the things we are told. You know, enough of being -- look at the Washington metro after billions of dollars. It's a disaster. How many things have to fail for the average American to finally decide the bureaucracy and the establishment can't deliver. Let's try something new.

SUSTEREN: Don't get me started on the D.C. metro system. Anyway, Mr. Speaker, thank you, sir.

GINGRICH: Good to be with you.