Ann Widdecombe won one of three seats for the Brexit Party in the South West of England, despite overall vote share tipping in favour of Remain parties.
The former MP said the result reaffirms the 2016 referendum and warned that if there was a general election the main parties would face "carnage".
However, combined results show remain parties the Lib Dems and Greens with 41.2% of the vote in the region.
The Liberal Democrats took two seats, with the Green Party taking one.
Martin Horwood and Caroline Voaden took the two Lib Dem seats, with Molly Scott Cato retaining a seat for the Greens.
The other winners for the Brexit Party were James Glancy and Christina Jordan.
Ms Widdecombe said: "It's very clear... there was only ever one reason for voting for the Brexit Party - and that is what the nation has done, big time.
"What this does is send a very clear message to Westminster - again - that if they don't sort out leave, at the next general election both the big parties are going to face carnage.
"We shouldn't even be having these elections. These elections are a clear demonstration of the farce that has enveloped Westminster.
"I want a clean Brexit and that is where we have to put our pressure."
Lib Dem MEP Mr Horwood, the former Cheltenham MP, said that the South West was "not such a leave region now".
He added that the "Lib Dems, Greens and Change UK beat Brexit Party and UKIP in the popular vote across the South West".
Green MEP Molly Scott Cato thanked supporters "for putting your trust in me again".
The Brexit Party took 36.7% of the vote, while the Conservatives lost more than 20% of their support in the region.
Of the remain parties, the Lib Dems were up by more than 12% while the Greens were up by 7% - giving the two parties 41.2% of the vote.
Boris Johnson's sister Rachel Johnson, who stood for Change UK, failed to win a seat.