What the home secretary and prime minister don't appear to understand is that the Windrush scandal is the direct effect of their policies and not just another example of the administrative chaos at the Home Office.
After repeated challenges to her testimony on the deportation of immigrants, Rudd telephoned May on Sunday and offered her resignation which was accepted, the source said.
Her handling of the controversy has been heavily criticised by MPs, with over 200 of them coming together to sign a letter accusing her of making up immigration policy in an effort to overcome the scandal.
The furor has grown since the Guardian newspaper reported that some people who came to the United Kingdom from the Caribbean in the decades after the Second World War had recently been refused medical care in Britain or threatened with deportation because they could not produce paperwork proving their right to reside in the country.
She was ultimately undone by the forensic probing of the Home Affairs Select Committee, when her evidence was contradicted by her own civil servants, who have now had their revenge. "I should have been aware of this, and I take full responsibility for the fact that I was not", Rudd said in the letter.
She claimed: "If you're asking me about numbers, that's not how we operate".
Rudd's position worsened after she told lawmakers last week that the government did not have targets for deporting people - only for a 2017 memo to emerge that mentioned specific targets for "enforced removals".
She was hauled before MPs and admitted they did exist.
Rudd's resignation comes four months after another close ally and her then most senior minister, Damian Green, was forced out of his job for lying about whether he knew pornography had been found on computers in his parliamentary office.
UK Home Secretary Amber Rudd resigns over Caribbean immigrant scandal
In modern times, only Theresa May has made the leap from Home Secretary to Prime Minister.
The UK Home Secretary Amber Rudd has resigned over reports she has personally set a target for an increase in the enforced deportation of immigrants.
The opposition Liberal Democrat party's home affairs spokesperson, Ed Davey, said Rudd had become "the fall guy to protect the prime minister".
"Theresa May must face questions now given these terrible failures largely took place under her watch as Home Secretary". May, who herself oversaw immigration policy when she ran the home office between 2010 and 2016, is yet to outline how immigration will work after Brexit.
May apologized to Caribbean leaders for any "anxiety" caused by the records destruction, which occurred when she was home secretary under the previous administration. We'll give her a huge welcome on to our back benches.
This was by far the most damaging admission by the Home Secretary, since it will reinforce the impression of her critics of incompetence and a failure to get a grip on the Home Office.
He called her "the Silver Spoon" in his columns because of her privileged background.
One leading bookmaker has installed Communities Secretary Sajid Javid as the early favourite, followed by Michael Gove, Jeremy Hunt, Karen Bradley and James Brokenshire.
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He projects to be embroiled in a punting battle with veteran Jon Ryan, who has four years left on his contract. Dissly arrived at Washington as a defensive end but transitioned to tight end for his final two seasons.