Labour Party MP David Lammy has co-ordinated some of the campaigning around the Windrush generation.
After Ms Rudd resigned, he said the campaign was "not just about political scalps" and her resignation "must not detract from the fact that this crisis was a direct result of the hostile environment policy".
Yesterday a letter from Mr Lammy and more than 200 other MPs called for government promises to Windrush migrants to be written in to law. It said promises the government made over compensation, housing or legal rights should be enshrined in law "without delay".
Replying to Ms Rudd's resignation letter, Theresa May wrote that she was "very sorry" to see her leave the Home Office and she should "take great pride" in what she had achieved.
Shadow Home Secretary Diane Abbott welcomed Ms Rudd's resignation.
She told 5 live's Stephen Nolan: "It was the right thing to do."
She added that the Labour Party was "determined to see justice for the Windrush generation, so in that sense it is not over."
Video content
Video caption: Shadow Home Secretary Diane AbbottShadow Home Secretary Diane Abbott
Windrush petition starter’s reaction
Patrick Vernon started a petition just over two weeks ago, calling for an amnesty for anyone arrived as a minor in the UK between 1948 to 1971.
He told BBC Radio 5 Live's Stephen Nolan: "Despite Amber Rudd leaving her post, the government still has a big job to do."
"I wasn't looking for a resignation... what the families want is their right as British citizens."
Video content
Video caption: Rudd: Patrick Vernon, who started the petition calling for Windrush amnesty, reactsRudd: Patrick Vernon, who started the petition calling for Windrush amnesty, reacts
Rudd 'should have known'
George Parker, the Financial Times' political editor, tweets that Amber Rudd's friends admit that "she should have known".
"With responsibility for immigration, counter-terrorism and policing, the job of home secretary is one of the toughest in government.
During one period under Labour, there were six home secretaries in eight years.
But Amber Rudd's job was made doubly difficult because she was following Theresa May, who'd survived in the post for more than six years and had set in train a series of plans and objectives that Ms Rudd was expected to stick to, even if she disagreed with them.
The former energy secretary was unable to put her stamp on any significant policy during her 21 months at the Home Office; much of her time was spent fire-fighting - dealing with the implications of Brexit, the rise in violent crime and last year's terror attacks.
Presentationally, Amber Rudd was impressive.
But she lacked a command of the detail, which her predecessor had mastered, and it proved to be her undoing."
Solidarity protests near Home Office
Before Ms Rudd's resignation, protests in favour of the Windrush immigrants were staged outside the Home Office in London.
EPACopyright: EPA
EPACopyright: EPA
Stories of the Windrush generation
BBCCopyright: BBC
One man was told he would have to pay for prostate cancer treatment as he didn't have the documents to show he was eligible for NHS treatment.
Another, who has been here for five decades - since she was 10 years old - got a letter saying she was in the country illegally and spent a week at Yarl's Wood immigration removal centre.
A third was a baby when he arrived in the UK but was told he did not "exist on any data in this country".
Video caption: Windrush deportation: Who are the Windrush generation?Windrush deportation: Who are the Windrush generation?
'Almighty problem' for Theresa May
Rob Watson
BBC political correspondent
"This is a big moment in British politics.
Amber Rudd's resignation is the result not just of the recent row over immigrants from the Caribbean - but allegations over her competence in managing the Home Office.
More important than the complexities of her resignation, however, is the almighty problem it leaves the Prime Minister.
Amber Rudd was one of the most pro-EU voices inside her deeply divided Cabinet, so does Theresa May replace her with another so-called remainer or an enthusiastic brexiteer?
It's a question that comes just as the government faces key and controversial decisions over the UK's future relationship with Brussels." .
How the Windrush row unfolded
Earlier this year, Labour peer Lord Faulkner raised the case of Paulette Wilson, who had come to Britain from Jamaica in 1968 and had been threatened with deportation
A number of similar cases were raised and, this month, a petition calling on the Home Office to grant them an amnesty garnered thousands of signatures
On Wednesday Ms Rudd told MPs investigating Windrush that there were no immigration removals targets
But an inspection report from December 2015 showed targets for voluntary removals did exist
Ms Rudd then admitted "local" targets for voluntary removals had been set
She told the Commons on Thursday she had not been aware of them
The Guardian then reported a June 2017 memo from an official, copied to Ms Rudd, that refers to targets
Quote Message: I have reviewed the advice I was given on this issue and become aware of information provided to my office which makes mention of targets.
I have reviewed the advice I was given on this issue and become aware of information provided to my office which makes mention of targets.
Quote Message: I should have been aware of this, and I take full responsibility for the fact that I was not.
I should have been aware of this, and I take full responsibility for the fact that I was not.
Rudd: I misled select committee
In her resignation letter, Ms Rudd said she "misled" MPs.
Quote Message: I feel it is necessary [to resign] because I inadvertently misled the Home Affairs Select Committee over targets for removal of illegal immigrants during their questions on Windrush.
I feel it is necessary [to resign] because I inadvertently misled the Home Affairs Select Committee over targets for removal of illegal immigrants during their questions on Windrush.
The "hostile environment" immigration policy has been blamed for the Windrush scandal.
Earlier this month, the government was forced to apologise after it emerged some children of the so-called Windrush generation had been declared illegal immigrants.
Many were threatened with deportation, denied access to NHS treatment, benefits and pensions and stripped of their jobs.
But what is the "hostile environment" policy?
Video content
Video caption: Windrush: What is the 'hostile environment' immigration policy?Windrush: What is the 'hostile environment' immigration policy?
Tributes pour in for "principled" Rudd
In the tributes tweeted by Amber Rudd's party colleagues following her resignation, a word that comes up repeatedly is "principled".
Live Reporting
Paul Gribben, Francesca Gillett and Claire Heald
All times stated are UK
'Not just about political scalps' - Lammy
Labour Party MP David Lammy has co-ordinated some of the campaigning around the Windrush generation.
After Ms Rudd resigned, he said the campaign was "not just about political scalps" and her resignation "must not detract from the fact that this crisis was a direct result of the hostile environment policy".
Yesterday a letter from Mr Lammy and more than 200 other MPs called for government promises to Windrush migrants to be written in to law. It said promises the government made over compensation, housing or legal rights should be enshrined in law "without delay".
Analysis: Several headaches for May
The loss of her home secretary has presented the Prime Minister with numerous problems, writes the BBC's political editor Laura Kuenssberg.
Theresa May 'very sorry' to see Amber Rudd leave
Replying to Ms Rudd's resignation letter, Theresa May wrote that she was "very sorry" to see her leave the Home Office and she should "take great pride" in what she had achieved.
Full text: Amber Rudd's resignation letter and Theresa May's response
Diane Abbott: 'It is not over'
Shadow Home Secretary Diane Abbott welcomed Ms Rudd's resignation.
She told 5 live's Stephen Nolan: "It was the right thing to do."
She added that the Labour Party was "determined to see justice for the Windrush generation, so in that sense it is not over."
Video content
Windrush petition starter’s reaction
Patrick Vernon started a petition just over two weeks ago, calling for an amnesty for anyone arrived as a minor in the UK between 1948 to 1971.
He told BBC Radio 5 Live's Stephen Nolan: "Despite Amber Rudd leaving her post, the government still has a big job to do."
"I wasn't looking for a resignation... what the families want is their right as British citizens."
Video content
Rudd 'should have known'
George Parker, the Financial Times' political editor, tweets that Amber Rudd's friends admit that "she should have known".
Home secretary job 'one of the toughest'
Danny Shaw
BBC Home Affairs Correspondent
"With responsibility for immigration, counter-terrorism and policing, the job of home secretary is one of the toughest in government.
During one period under Labour, there were six home secretaries in eight years.
But Amber Rudd's job was made doubly difficult because she was following Theresa May, who'd survived in the post for more than six years and had set in train a series of plans and objectives that Ms Rudd was expected to stick to, even if she disagreed with them.
The former energy secretary was unable to put her stamp on any significant policy during her 21 months at the Home Office; much of her time was spent fire-fighting - dealing with the implications of Brexit, the rise in violent crime and last year's terror attacks.
Presentationally, Amber Rudd was impressive.
But she lacked a command of the detail, which her predecessor had mastered, and it proved to be her undoing."
Solidarity protests near Home Office
Before Ms Rudd's resignation, protests in favour of the Windrush immigrants were staged outside the Home Office in London.
Stories of the Windrush generation
One man was told he would have to pay for prostate cancer treatment as he didn't have the documents to show he was eligible for NHS treatment.
Another, who has been here for five decades - since she was 10 years old - got a letter saying she was in the country illegally and spent a week at Yarl's Wood immigration removal centre.
A third was a baby when he arrived in the UK but was told he did not "exist on any data in this country".
Here are the stories of the people affected by being incorrectly identified as being illegal immigrants.
Who are the Windrush generation?
Video content
'Almighty problem' for Theresa May
Rob Watson
BBC political correspondent
"This is a big moment in British politics.
Amber Rudd's resignation is the result not just of the recent row over immigrants from the Caribbean - but allegations over her competence in managing the Home Office.
More important than the complexities of her resignation, however, is the almighty problem it leaves the Prime Minister.
Amber Rudd was one of the most pro-EU voices inside her deeply divided Cabinet, so does Theresa May replace her with another so-called remainer or an enthusiastic brexiteer?
It's a question that comes just as the government faces key and controversial decisions over the UK's future relationship with Brussels." .
How the Windrush row unfolded
Rudd's resignation - the papers' take
Amber Rudd's resignation dominates the front pages of Monday's newspapers.
Her "denials are in tatters", the Telegraph writes.
See the front pages here.
Rudd: I take full responsibility
More from Amber Rudd's resignation letter.
Rudd: I misled select committee
In her resignation letter, Ms Rudd said she "misled" MPs.
Resignation letter in full
Here's Amber Rudd's resignation letter in full:
What is 'hostile environment' immigration policy?
The "hostile environment" immigration policy has been blamed for the Windrush scandal.
Earlier this month, the government was forced to apologise after it emerged some children of the so-called Windrush generation had been declared illegal immigrants.
Many were threatened with deportation, denied access to NHS treatment, benefits and pensions and stripped of their jobs.
But what is the "hostile environment" policy?
Video content
Tributes pour in for "principled" Rudd
In the tributes tweeted by Amber Rudd's party colleagues following her resignation, a word that comes up repeatedly is "principled".
Who is Amber Rudd?
Amber Rudd is a former investment banker and financial journalist, who decided to enter politics in her 40s.
She rose rapidly through British politics, becoming home secretary only six years after being elected an MP in 2010.
Ms Rudd - an Edinburgh University history graduate - has two children from the five years she was married to columnist AA Gill.
They separated in 1995. Gill died in 2016.
George Osborne 'so so sad'
Former chancellor George Osborne reacts: