Speaking at the Institute for Government in London on Monday, Ms Rayner announced plans to ban all second jobs, create a new Office for Value for Money and pledge to reform the public procurement system.
She said: "The current regime is no longer working precisely because we have a Prime Minister who is shameless in breaking the rules and won't enforce consequences on others who break them.
"Corruption – that is the word – is happening in plain sight and it is rife right through this Conservative government.
"Why do the rules and standards matter? Because the people who are picking up the bill for this corrupt government are the taxpayers whose money ministers are wasting and abusing.
"Our democracy cannot hinge on gentleman's agreements. It needs independent and robust protection from Conservative corruption.
"Boris Johnson's corruption means that we must now urgently rebuild trust in our politics, in public office and in government as a force for good. That means rebuilding the regime that is not working.
"The British people deserve so much better than Boris Johnson's corruption and failure."
The proposals would also stop the revolving door between government and the companies that ministers are supposed to regulate with a ban for five years after leaving office.
It would also strengthen the government standards system with a new independent integrity and ethics commission to defend and extend standards in government.
A Cabinet Office spokesman said: "The government has committed to continually reinforcing high standards of conduct in public life so the public can have trust and confidence in the operation of government at all levels.
"As we have said previously, we will carefully consider the reports by the Committee on Standards in Public Life, Nigel Boardman and others, before setting out a full update to Parliament in due course.
"It's absolutely right that we fully take account of all of the evidence and work up the best solutions before responding."
The Labour pledges came during a speech that appeared to see Ms Rayner blindsided by a shadow cabinet reshuffle taking place as she delivered her speech.
During the question-and-answer session after Ms Rayner’s speech, Labour shadow cabinet member Cat Smith confirmed the reshuffle had started by writing on Twitter that she would be resigning and returning to the backbenches.
The fact Sir Keir was about to act was also being widely reported as Ms Rayner spoke.
Following the speech, a spokesperson for Sir Keir confirmed a reshuffle was under way.
Asked after her speech about Sir Keir’s move, Ms Rayner said she did not “know the details of any reshuffle”, but that “we need some consistency in how we’re approaching things as an opposition”.
However, a shadow cabinet source later accused Ms Rayner of pretending not to know about it.
They said: "This is all very curious. Angela has been telling us she would sort a reshuffle for months and that Keir couldn't do it without her.
"And now it happens she's saying she knew nothing about it."
A row over internal reforms during the Labour Party conference in September also overshadowed Ms Rayner’s appearance on the event’s main stage.
In her resignation letter, Ms Smith, the Lancaster and Fleetwood MP, wrote: “You will be aware that we had a meeting scheduled for later this week, during which I wanted to raise the issue of, and my concerns about, Jeremy [Corbyn] not being readmitted to the Parliamentary Labour Party after he was readmitted into our party membership following due process.
“This position is utterly unsustainable and it is important that you truly understand how much damage this is causing in constituency Labour Parties and amongst ordinary members, a number of whom are no longer campaigning.”
Shadow culture secretary Jo Stevens has also replaced Nia Griffith as shadow Welsh secretary as part of the reshuffle.