London — As British Prime Minister Boris Johnson tries to get his Brexit deal passed by Parliament, the new Brexit Party, led by Nigel Farage, is campaigning for the United Kingdom to leave the European Union without an agreement. They're calling for a "clean-break" Brexit, but for many Brexit Party supporters, who have come from both sides of the political aisle, Brexit means more than just taking Britain out of the EU.

"(Brexit has) shown Parliament to be an embarrassment to Britain. And to democracy," Lesley Quigly told CBS News at a Brexit Party rally on Friday night.

"Whichever way it goes, I'll always be a supporter of the Brexit Party," said Michel Henry, who was also attending the rally.

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"(Parliament) don't represent anybody," Adam Price, from London, told CBS News. "All they represent is their own selfish interest."

"Breaking down" the left-right divide

Brexit has redrawn the lines of traditional political affiliations in Britain. Many people now identify as "leavers" or "remainers" above anything else, and the subject of the U.K. leaving the EU often serves as an entry point for a number of other issues, including a growing skepticism of the political status quo.

"It's led to quite a big breaking down of the old left-right divides," Farage, who took over as Brexit Party leader in March, told CBS News. "It's also, as of now, led to the most incredible disconnect between Parliament and the people."

The Brexit Party was created in January of this year, and polling showed a growth in support during the tenure of former Prime Minister Theresa May. When Britain went to elect new representatives to the EU in the spring, the Brexit Party got more votes than any other British political party. Their next mission is to get candidates elected to Britain's own Parliament.

Sam Gyimah is a current member of Parliament (MP), but Prime Minister Boris Johnson kicked him out of their traditional Conservative Party for rebelling against a recent piece of Brexit legislation. Gyimah switched to a different party — the Liberal Democrats — who want to cancel Brexit and keep Britain in the EU.

"Brexit is like a meteor that has struck British politics, and the pieces are all over the place," Gyimah told CBS News. "But where people traditionally used to identify politically as on the left or on the right of the political spectrum, they now identify as leave or remain. That is the big divide on British politics today, and it's not going away anytime soon."

Polling shows support for the Brexit Party's has gone down recently, possibly because Boris Johnson, who is viewed as more aggressive on Brexit, became prime minister. But Farage doesn't think his party is going away.

"There's an appetite for Brexit amongst those that voted Brexit and amongst those who didn't vote for Brexit," Farage told CBS News. "There's an appetite amongst all people for political reform, for completely getting rid of the current system we've got."

Shooting producer Andy Hayward contributed to this report.