"It's the same game. Both Brexit and Trump were huge seismic shocks in the political arena and just as our [members of parliament] here don't accept Brexit, many of them want to stop it or overturn it," Farage told "Fox & Friends."
"In America, you've got large sections of the media and of the left who do not accept the legitimacy of this president, do not believe could possibly have won by fair means, and come up with endless conspiracy theories about Russia or whatever else it may be. I think the parallels are remarkable."
Britain’s House of Commons voted Thursday to ask the European Union to delay their country’s exit.
"The problem is hundreds of our members of parliament didn't only vote the other way but they have never ever respected the result and are doing their best to overturn it, to frustrate it," Farage told co-host Steve Doocy.
"And in the middle of all this Theresa May has made the most holy mess of the thing by putting on the table a document that is completely unacceptable."
Britain, by law, will leave the EU on March 29 with or without a deal, unless it cancels Brexit or secures a delay.
Pro-Brexit lawmakers in Prime Minister May’s Conservative Party have rejected her withdrawal deal, which outlines a future relationship with the EU, believing it restricts them.
"This is one of the oldest functioning democracies in the world and our democracy is being walked all over. It's one of the most shameful episodes in the history of my country," Farage said.
"In the end it's up to our prime minister, if she was bold or brave we'd still leave in two weeks time. But I'm afraid she's buckling to political pressure and it looks like there's going to be a delay to Brexit and that's going to make this country very, very angry indeed."
The Associated Press contributed to this report.