In her victory speech, Badenoch promised to “renew” the party and told cheering supporters it was “time to get down to business”.
The BBC spoke to people in the centre of Saffron Walden to find out their reactions to their local MP being elected party leader.
One said: “I am very happy. She is very straightforward. When she was going for the leadership, it was about the principles and not policies. Go Kemi!”
Another constituent said: “We need more women in power. More black women. It’s a first and we need the change.”
But a trader at the market said: “She is not a good MP. She is not interested in Saffron Walden. She is only interested in herself.”
Another woman said: “She is arrogant and rude and very attacking. All in all, very disappointing but [I’m] not surprised she has become the leader.”
Mr Sinclair said: “The Conservative Party is very battered. The job facing Kemi Badenoch now is to find a narrative that will win back those people who used to vote Conservative but also win new supporters for the Conservative Party. That is going to be by no means a very easy feat.”
He added: “She has got a pretty good reputation within the constituency of North West Essex for being a good constituency MP.
“The key to success when you become a minister or if you become a party leader is to have a strong, local team behind you, and as far as I can tell she has quite a strong constituency team.”
The BBC understands Badenoch plans to reveal her shadow cabinet by Wednesday, ahead of the critical Budget vote and her debut clash with Sir Keir Starmer at Prime Minister’s Questions.
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