The former London Assembly member said she wanted to 'tell the truth' in office.
Senior Conservative backbencher Tom Tugendhat has also launched a leadership bid - four MPs have so far done so.
Sir Charles Walker, a former joint acting chairman of the 1922 Committee of backbench Tory MPs which will set the rules for the contest, says he anticipates a shortlist of two candidates will be known by 21 July, when Parliament breaks for the summer. The 42-year-old MP for Saffron Walden - who was among those to resign their government jobs this week - said she would lower taxes, but also have a "tight spending discipline".
She said "people are exhausted by platitudes and empty rhetoric" and an "intellectual grasp of what is required to run the country" is missing. Several senior Tory MPs have endorsed Mr Sunak's campaign, including Oliver Dowden, Mark Spencer and Liam Fox.
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