Systemic racism is in the government as well as much of society and Theresa May – who 'is not behaving like a Christian' over immigration – should apologise or resign, the campaigning MP David Lammy has said.

Speaking to Christian Today in the context of the Windrush scandal, Lammy, who is himself a practising Christian, said that May 'took pleasure' in creating a 'hostile environment' for immigrants when she was home secretary.

'This is about the zeal with which Theresa May as home secretary embarked on creating a hostile environment and took pleasure in that, egged on by people like Nigel Farage,' the MP for Tottenham said.

Lammy said of the prime minister: 'Theresa May feels like a politician with no conviction. She blows with the wind. She is a politician who is pragmatic to the point of weakness. Does she stand for something? And if she does then she should explain what she stands for – she should apologise or resign.

'Theresa May is not behaving like a Christian – this is not Christian, what has happened. These are not the Christian values I learned at Sunday school.'

Lammy was speaking as church leaders across the UK condemned the government's handling of thousands of people from around the Commonwealth came to the UK after the Second World War to fill a labour shortage. The 1971 Immigration Act ended the free movement between Commonwealth nations that had existed until that point but gave all Commonwealth citizens living in the UK the right to remain. However the Home Office did not keep a record of those given leave to remain meaning they now find themselves having to prove they are here legally without having the paperwork to do so.

'Right across the country people of all political persuasions are all offended by the stories that are coming out,' said Lammy.

Asked about racism in modern Britain, he said: 'Race is a construct. There is only one race – the human race – and the heart of modern day racism is a construct, systemic, based on white supremacy. And it is not confined to extremist groups. It is based on the idea that with colonisation there is one group superior to others.

'It is a virulent disease that affects much of society and is persistent.'

Asked whether the systemic racism extends to the government as well as elements of the media, Lammy said: 'Of course – I'm very clear about that.'

He added: 'We make big strides forward in society but then it's very easy for things to go backwards.'

In a reference to the spate of gun and knife killings in the capital this year, he said: 'I have spent the last two weeks in the public eye in part because of 50 deaths in London – and it is deeply troubling that it took 50 deaths for people to care about young black lives in London.

'I had to seek quite strongly to get the home secretary [Amber Rudd] and mayor [of London Sadiq Khan] to act. And here we are with the Windrush generation, campaigning hard, with the help of some fantastic journalists such as Amelia Gentleman [of the Guardian], and it's similar.

'And the campaign has caught fire. But again you have to ask why you have 60-year-olds being denied cancer treatment despite paying their bills for decades,' added Lammy, in a reference to 63-year-old Albert Thompson, who was told he would have to pay £54,000 for prostate cancer treatment unless he could produce documentation.

Lammy, who has called for a comprehensive review of immigration policy, said that 'there is systemic, institutionalised racism which is persistent' and added: 'There has to be a review – we have to re-examine our values.

'Look at the faces of the Windrush generation and it forces you to re-examine our values. But I want to see not just a U-turn on Windrush but on the "hostile environment" policy which, since 2013, has made life as difficult as possible for individuals without the correct papers to live in the UK.

'As I said to Amber Rudd in the House, if you lay down with dogs, you get fleas,' Lammy added in a reference to Tory immigration policy influenced by the hard right.

Asked if it is harder for black people to be seen as British by wider society, Lammy said: 'When [the retired athlete] Jessica Enis-Hill wrapped herself in a British flag everyone was delighted that she is British. Of course these people are British – they are British subjects but, are they allowed also to be English? Or is Englishness confined to ethnicity and a racial definition?'

He went on: 'In a post Brexit environment there are elements in the country who want to define being British or English as a white Anglo-Saxon background.

'What we are seeing across the world is a reactionary spasm – Trump in the US and here.'

Lammy concluded: 'As Christians, you know the story of Jesus, born a refugee in a dirty out-house surrounded by animals, fleeing Herod. It's always important to stand up for the other, those who are different in society, those who come from somewhere else, often escaping hardship.

'The Windrush generation are the descendants of enslaved people who were then colonised who were made British subjects. It is an outrage given they are people who served our country in World War One and World War Two, invited to help rebuild the country, build the NHS and transport system  –that they should be sent back across the ocean 70 years later.'