Mel Stride has been knocked out of the race to succeed Rishi Sunak as Conservative party leader after Robert Jenrick topped the poll of MPs for the second time. The former work and pensions secretary on Tuesday became the second casualty in the extended leadership contest, which is due to culminate in early November. The four surviving candidates – Jenrick, Kemi Badenoch, James Cleverly and Tom Tugendhat – will now be subject to a “beauty contest” at the Conservative conference in early October, where they will make their case to party members. Stride, a Sunak loyalist, got 16 votes from colleagues on Tuesday, finishing bottom of the remaining five MPs vying for the leadership after Priti Patel was knocked out in the first round last week. Once again Jenrick, a former immigration minister, finished top of the closely contested ballot, collecting 33 votes, up five on the first round. Badenoch came second with 28 votes, up six on the previous round. Cleverly and Tugendhat were joint third place with 21 votes each. Cleverly’s number of votes stayed steady while Tugendhat’s tally went up by four. There were 119 votes cast by Conservative MPs in total, with no spoilt ballots. After their party conference in Birmingham, Conservative MPs will hold further rounds of voting to whittle down the list of candidates to a final two, with the winner to be decided by a vote of the grassroots membership. Members of Tugendhat and Badenoch’s campaigns claimed that their candidates had the most momentum going into conference. The fact that Cleverly’s number of votes did not change suggests he lost supporters, as two of Patel’s backers – Greg Smith and Alec Shelbrooke – publicly switched to him. Cleverly and Tugendhat, who are seen as centrists, are likely to mop up some of Stride’s supporters. Strategists on two other rival camps said Stride was suspected of privately working with Jenrick, however. Cleverly’s allies suggested some of the MPs who voted for him during the previous round may have switched to Tugendhat to ensure they both made it to the final four. Some One Nation Conservatives are likely to argue that they should now unite behind either Tugendhat or Cleverly to try to stop a final runoff between Badenoch and Jenrick. Jenrick has pitched himself as a rightwinger with hardline views on immigration. Badenoch made a name for herself in government by being outspoken on gender and culture war issues, and polls suggest she is the most popular candidate with the grassroots. She topped a shadow cabinet survey rating on the ConservativeHome website on Tuesday, with Cleverly and Tugendhat in second and third place. A Badenoch campaign spokesperson said: “Kemi has the momentum – she’s putting on votes from right across the party, has more shadow cabinet backers than the other candidates combined, and the independent polling shows she is overwhelmingly the choice of the party membership. The Conservatives need a leader with the star power to cut through, take the fight to Labour and lead us back to government. Kemi is that leader.” Cleverly, a former foreign and home secretary, said he was “proud to be through to the final four and grateful for the support of my Conservative colleagues. We must unite our party with Conservative values, and take the fight to Labour. The work continues.” Tugendhat thanked his supporters and said his party had “a simple choice: we can choose someone who has service at their core, who is a proven leader and who acts on their principles, or we can expect more of the same”. His allies said he had a huge amount of momentum. Jenrick said: “In opposition you have a choice: you can either do the easy thing and carry on as before, or you can listen to the country, recognise your shortcomings, and change. I’m grateful that so many colleagues have chosen the latter, hard though it may be.” Under plans drafted by Conservative Campaign Headquarters (CCHQ), the four candidates will reportedly only be given 10 minutes each to make their pitch from the main stage at the conference. The results were announced by Bob Blackman, the chairman of the 1922 Committee of Tory backbenchers, in a press conference on Tuesday afternoon. Stride was a regular fixture on television and radio during the election, but was relatively little known compared with some of his more high-profile leadership rivals. He was the only one of the six not to officially launch his campaign before the first round of voting, saying he would only do so if he made it through to later rounds.