LONDON (Reuters) - Reform UK, the right-wing populist party led by Nigel Farage, looks set to emerge as a new force in British politics, with an election exit poll on Thursday predicting it would win 13 seats, and early results showing it was squeezing the Conservative vote.

Farage, a driving force behind Britain's decision to leave the European Union, only entered the election race last month, a move that caused shockwaves in a Conservative Party that was already far adrift of centre-left Labour.

In the first three results to be declared, Labour won comfortably, with Reform finishing in second place and Prime Minister Rishi Sunak's Conservatives pushed into third. 

It took 29% and 27% of the vote in the first two counts, prompting Farage to say: "That is way more than any possible prediction or projection, it's almost unbelievable."    

Farage's party aims to shake up British politics as Marine Le Pen's National Rally is doing in France by taking a tough line on immigration, demanding that illegal migrants arriving in small boats from France are sent back. 

That would be difficult to achieve, but by focusing on the issue, it has targeted a weak spot for the Conservatives, which have failed to "stop the boats" as promised by Sunak.    

The Conservative plan to deport asylum seekers to Rwanda also failed to get off the ground before the election was called.

Polling company Savanta's Political Research Director Chris Hopkins said if the exit poll was right, it would be "dream scenario" for Farage. 

"He'll be rubbing his hands with glee," he said. "He's got enough MPs (lawmakers) to make a racket in Westminster, and the party he shares the closest political space with could be reduced to a long period of soul searching. 

"It could be that Reform UK is second in a huge number of seats."

(Reporting by Paul Sandle; Additional reporting by Muvija M; Editing by Toby Chopra)

By Paul Sandle