Party figures say frontrunner will be brought down by the right if he tries to move to more moderate ground

Robert Jenrick at the Tory party conference in Birmingham. Photograph: Christopher Thomond/The Guardian

Robert Jenrick will be toppled by the Tory party’s right wing should he attempt to pivot to the centre ground if installed as leader, senior Conservatives have warned.

Jenrick, who remains the frontrunner for the job after the party’s conference in Birmingham, has won support from the right with a series of uncompromising stances. He has said he would welcome Nigel Farage into the party, leave the European convention on human rights and vote for Donald Trump.

Having started life as an MP as a moderate, some believe he has only temporarily adopted a more rightwing stance as part of his efforts to win the leadership. Some allies have suggested he will move back to the centre once in office.

However, senior party figures are already warning Jenrick that if he becomes leader, his fate will be in the hands of rightwing MPs willing to attack those who have attempted to move away from their agenda.

They warned that he had entrusted his fate to the “Braverman right” – a reference to the former home secretary, Suella Braverman. Jenrick was made immigration minister under Braverman in the expectation that he would be a moderating force. However, he is said to have been radicalised by his time in the Home Office on the need for tougher policies.

One shadow minister compared Jenrick to Iain Duncan Smith, the former Tory leader delivered into power by the right, but ultimately unable to widen his appeal to voters. Duncan Smith was removed as leader after just over two years.

“What will happen to him is that he will suffer the fate of IDS,” they said. “He will try to pivot to the centre, but what he’ll find is that the Braverman right won’t let him. They would pull their support and threaten to submit their latest vote of no confidence for a leadership contest. They have got him by the balls. It now only takes 19 letters to prompt a confidence vote in the leader.”

Allies of Jenrick strongly disputed the idea, pointing out that the likes of Victoria Atkins, Ed Argar and John Lamont – Tory figures associated with the liberal, One Nation wing of the party – also backed his leadership bid.

Jenrick bolstered his credentials with the party’s grassroots during the conference by confirming that his daughter’s middle name was Thatcher. He has also appeared in a hoodie emblazoned with the words “Hamas Are Terrorists”.

MPs will whittle down the four remaining candidates to two this week. Those two will then be put forward to a vote of party members. While Jenrick remains favourite, a small number of MPs changing their vote could have a major impact. James Cleverly, shadow home secretary, was thought to have had a good conference after calling on the party to be “more normal”.

However, there are sobering revelations about the party’s relevance to the public in the latest Opinium poll for the Observer. It reveals that more of the public were aware of Phillip Schofield’s return to TV in his programme Cast Away than had heard about the Conservative conference. Labour still leads in most policy areas with the public, though the two main parties are now tied on the economy.

Among those giving a view, Cleverly was deemed to have had a good conference, seeing an improvement in his “acceptability” score and is currently the frontrunner among the wider British public.

Kemi Badenoch has taken the biggest knock to her public perception. She received criticism last week for suggesting maternity pay was “excessive”. Half (49%) of 2019 Conservative voters say Cleverly would be an acceptable leader of the Conservative party, with 41% saying the same of Jenrick, 40% of Tom Tugendhat and 37% of Badenoch.

Adam Drummond, head of political and social research at Opinium, said: “To nobody’s surprise, voters are not paying a great deal of attention to the Conservative leadership contest and it is notable that, as unpopular as the Labour government already is, voters prefer them over the Tories on almost all issues, with the two parties tied on the economy.”