Asked if she should take some personal responsibility for 52-year-old Rudd's resignation, May said today: "When I was home secretary, yes, there were targets in terms of removing people from the country who were here illegally". May - under whose Home Office tenure the "hostile environment" policy was introduced - over the Windrush row.
A government clampdown on illegal immigration has begun to identify those without papers, scooping up many elderly people from the Windrush generation - named the ship that brought the first group of migrants from the West Indies in 1948.
Sajid Javid is not particularly a close ally of the prime minister herself.
"The architect of this crisis, May, must now step forward to give an immediate, full and honest account of how this inexcusable situation happened on her watch", said Diane Abbott, Labour's spokeswoman on interior affairs.
Amber Rudd's denial that there were "targets" for the expulsion of immigrants - despite all evidence pointing to the contrary - became too much after the Windrush affair.
But in recent years, successive British governments have sought to appear tough on illegal immigration, and their descendants are now struggling to prove a citizenship status they previously took for granted.
The Windrush Generation, migrants from the Caribbean who relocated to the U.K.at the end of World War II and helped to rebuild the country, were denied healthcare and pensions, with some being threatened with arrest and deportation, due to not possessing the correct documents.
And he said he would not be using the phrase "hostile environment" to describe immigration laws introduced by Theresa May when she was home secretary.
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"That's why I am so personally committed to and invested in resolving the difficulties faced by the people of the Windrush generation who have built their lives here and contributed so much". The prime minister doesn't have a majority in the United Kingdom parliament and is struggling with Brexit negotiations.
Immigration is a divisive issue in Britain, with cutting the inflow of migrants a major factor for many voters who in 2016 backed leaving the European Union.
The main opposition Labour Party accused Rudd of being a "human shield" for May.
While interior minister between 2010 and 2016 May pioneered controversial policies meant to create a "hostile environment" for people in Britain illegally.
Rudd said she didn't see the memo, but The Guardian later published a leaked letter she wrote to the prime minister discussing an aim of increasing removals by 10 percent.
In a Sunday interview which looks like his audition for the job, or an official introduction before Ms Rudd was out of the door, Mr Javid acknowledged his Pakistani parents or indeed he could have fallen victim to the Home Office's wrongful and aggressive questioning of Commonwealth citizens' immigration status.
He said: "First of all Mr Speaker can I thank the right honourable lady for her kind remarks at the start". Actually, they were always British.
The prime minister has replaced Rudd in the Home Office with former communities secretary Sajid Javid.
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