UKIP leader Nigel Farage has warned of disturbances on the streets if Parliament tries to block Brexit.
He told BBC One's Andrew Marr Show there would be "political anger the likes of which none of us in our lifetimes have ever witnessed".
The comments follow the High Court ruling that MPs and peers must have a vote ahead of the government triggering official talks with the European Union.
The campaigner who brought the case said it had given "clarity".
Mr Farage is in charge of UKIP on an interim basis, as the party looks for its next full-time leader, following the resignation of Diane James after just 18 days in the job.
The judges who ruled on Thursday that the government must seek MPs' approval to invoke Article 50 of the Lisbon Treaty - getting formal Brexit negotiations with the EU under way - have been criticised in some newspapers, the Daily Mail calling them "enemies of the people".
Mr Farage said: "We may have seen Bob Geldof and 40,000 people in Parliament Square moaning about Brexit.
"Believe you me, if the people in this country think they're going to be cheated, they're going to be betrayed, then we will see political anger the likes of which none of us in our lifetimes have ever witnessed in this country. Those newspaper headlines are reflecting that."
Asked by Andrew Marr if there was a danger of "disturbance in the streets and so on" if Parliament thwarted Brexit, Mr Farage replied: "Yes, I think that's right."
He added: "The temperature of this is very, very high.
"Now, I'm going to say to everybody watching this who was on the Brexit side - let's try and get even, let's have peaceful protests and let's make sure in any form of election we don't support people who want to overturn this process."
Also appearing on Andrew Marr, investment manager Gina Miller, who brought the High Court case against the government, insisted the UK had a representative democracy which ensured politicians had to debate issues.
"Do we want a country where we have no process?" she asked, adding: "The case is that [Mrs May] cannot use something called the Royal Prerogative to do it because we do not live in a tin-pot dictatorship."
She told Mr Farage: "That's what you argued for the whole way through [the Brexit referendum campaign] - parliamentary sovereignty."
He replied: "No, no. This is not about whether Parliament is sovereign; it's about whether the British people are sovereign."
Liberal Democrat leader Tim Farron criticised Mr Farage over his warnings of disturbances, saying "all responsible politicians" must distance themselves from UKIP's leader.
He said: "This is the politics of the gutter. All that has happened is that British judges in a British court have interpreted British laws.
"Nigel Farage should welcome that. British citizens aren't talking about taking to the street, only Nigel Farage is.
"Responsible leaders have a duty to calm tempers, heal division and work together to keep Britain open, tolerant and united."
Meanwhile, Mr Farage told Andrew Neil he was "sick" of and "finished" with party politics but would continue campaigning on "issues" after leaving frontline politics.
Several contenders have quit the leadership contest, leaving Suzanne Evans, Paul Nuttall and John Rees-Evans.
Mr Farage described the situation as a "soap opera" over a "terrible few weeks", but said the party was still well-placed in the opinion polls.