Divisions over the future of May was made public on Friday with a former chairman of her party saying 30 Conservative members of parliament backed a plot to topple her.
John Griffin, the founder of taxi firm Addison Lee who has given more than £4 million to the Tories, said he wanted May to remain as PM and called for Johnson to be given a "smacked bum" for undermining her.
May began her speech by talking about why she joined the party 40 years ago, highlighting that the things that have made her most proud have not been the positions held but "knowing that I made a difference - helped those who can not be heard".
The party's poor showing in the June snap election when May lost her overall majority in the House of Commons had already weakened her position.
May is facing calls from some colleagues to step aside after a disastrous election campaign earlier this year and a shambolic speech to her party's annual conference on Wednesday that was disrupted first by a prankster and then an uncontrollable coughing fit.
May's speech was also marred by a comedian - who mid-way handed her a P45 (better known as the letter of termination of employment) - and letters falling off the bold slogan behind her. She set out her main principles in a major speech in Florence last month, but the issue continues to divide her party.
Graft accused Nawaz set to return as PML-N chief
Besides Nawaz, his children Hussain, Hassan and Maryam, and son-in-law Mohammad Safdar, are also accused of corruption.
Gove added: "The truth is that the entirety of the cabinet want the prime minister to concentrate on doing the job".
They said the "image of her leaving Downing Street with tears in her eyes" would have a profound effect on the party.
Shapps said in media interviews: "I believe Theresa May is very decent person and unfortunately fought an election that didn't work out". "[Foreign Secretary Boris Johnson] told me to hand her a P45", the prankster said afterward. "I was about to talk about someone I want to give a P45 to: Jeremy Corbyn", she said to a standing ovation. "The solution is not to bury heads in the sand", he said.
Backbencher Mark Pritchard suggested a "small number" of colleagues were raising questions over her leadership in text message exchanges and warned them "there is no vacancy at Number 10".
The Prime Minister also said it will invest an additional £2 billion (S$3.6 billion) in affordable housing - taking the total affordable housing budget to nearly £9 billion.