LONDON, Jan. 23 (Reuters) - Senior British Conservative lawmaker Simon Clarke called on Tuesday for a change of prime minister, saying Rishi Sunak was leading the governing party into an election later this year "where we will be massacred".

Since Sunak pushed through his Rwanda immigration plan last week, ignoring the demands of several in his party's right wing to toughen it, some have been increasingly vocal in their criticism of the British leader, fearing he has little chance of reducing the opposition Labour Party's lead before the election.

But Clarke's words, while welcomed by a few, were sharply criticised by some on the right wing, who said it was not the time for yet another leadership contest after the Conservatives had ousted three prime ministers in less than 5 years.

Sunak, in power since 2022, has called on the party to unite before the election, which he expects to come in the second half of the year, saying its deep divisions and years of infighting are doing little for its fortunes in the opinion polls.

In a column for the Daily Telegraph newspaper, Clarke did little to ease those divisions by calling on other Conservative lawmakers to oust Sunak: "Now is not the time to despair. It is the time to act."

"A change of leadership would not have to be a protracted affair," he said, adding it could take a week and that "extinction is a very real possibility" for the Conservatives if Sunak leads the party into the election.

"We have a clear choice. Stick with Rishi Sunak, take the inevitable electoral consequences, and give the Left (Labour) a blank cheque to change Britain as they see fit. Or we can change leader, and give our country and party a fighting chance."

He said some would say another leadership contest would be ridiculous, "but what could be more ridiculous than meekly sleepwalking towards an avoidable annihilation because we were not willing to listen to what the public are telling us so clearly?."

Clarke, who was the levelling-up minister under Britain's former leader Liz Truss, left government when Sunak became prime minister in 2022 and has become a leading critic of his plan to deport asylum seekers to Rwanda.

He, like some others in the party, say Sunak's proposed legislation will not work and would allow asylum seekers to use the courts to stop their deportations and undo the plan, leading to electoral defeat.

Sunak says the legislation is the toughest immigration plan ever to be brought into British law, shrugging off criticism from legal experts who say it sails too close to breaching international human rights law.

While some Conservatives share Clarke's anger, others on the right of the party said it was not the time for "self-indulgence".

"At this critical time for our country, with challenges at home and abroad, our party must focus on the people we serve and deliver for the country," said Priti Patel, a former interior minister who alongside former Prime Minister Boris Johnson started the Rwanda plan.

"Engaging in facile and divisive self indulgence only serves our opponents, it's time to unite and get on with the job."

Labour said the Conservatives should quit.

"There are many good reasons for getting rid of this clapped out Conservative government and liberating the British people from endless bouts of Tory infighting is certainly one of them," said Pat McFadden, Labour's National Campaign Coordinator.

"Whilst the Conservatives fight among themselves, Labour will fight for a better future for the country."

Photo from Reuters