Jeremy Corbyn has written to Theresa May to demand the public inquiry into the Grenfell Tower fire is widened to cover social issues linked to the disaster.

The Labour leader said he was “deeply concerned” that the inquiry, led by Sir Martin Moore-Bick, will not consider issues such as social housing, austerity and deprivation linked to the fire, which left at least 80 people dead.

The terms of reference of Mr Moore-Bick’s investigation were announced earlier in the week after Ms May accepted the retired judge’s recommendations on what it should cover.

While the inquiry will focus on the immediate causes of the Grenfell fire and the broader regulations relating to high-rise buildings, wider issues about housing and poverty will not be included in its remit.

In his letter, Mr Corbyn suggested the nature of the inquiry is a sign that Ms May’s priority is “to avoid criticism of your party’s policy failures rather than secure justice for Grenfell survivors”.

He said: “I am deeply concerned by the decision to exclude the broader social and political issues raised by the fire from the terms of reference of the inquiry. The fire has raised profound concerns about the way that social housing is provided and managed in this country, and I – as well as many survivors – worry that, without a wider focus, the inquiry will fail to get fully to grips with the causes of the fire.

“The fear is that the priority is to avoid criticism of your party’s policy failures rather than secure justice for Grenfell survivors, along with the safety of the many other people who live in social housing in this country.”

In Pictures: Grenfell Tower after the fire Show all 51 1 /51 In Pictures: Grenfell Tower after the fire In Pictures: Grenfell Tower after the fire Police have released images from inside the tower where at least 58 people have died Metropolitan Police In Pictures: Grenfell Tower after the fire A still from a video shared by polices what appears to be a stationary bicycle sitting among the ashes In Pictures: Grenfell Tower after the fire A still from a video shared by police shows the remnants of a burnt-out bathroom In Pictures: Grenfell Tower after the fire Picture showing the lifts on an unknown floor Metropolitan Police In Pictures: Grenfell Tower after the fire Emergency crews outside the front entrance to the tower Metropolitan Police In Pictures: Grenfell Tower after the fire Fire crews inspecting flats in the burnt out tower London Metropolitan Police In Pictures: Grenfell Tower after the fire Grenfell Tower is seen in the distance PA In Pictures: Grenfell Tower after the fire A drone flies near the scene of the fire which destroyed the Grenfell Tower block REUTERS/Stefan Wermuth In Pictures: Grenfell Tower after the fire 'Theresa May Stay Away' message written on the messages of support at Latymer Community Church for those affected by the fire Ray Tang/REX In Pictures: Grenfell Tower after the fire An aerial view of the area surrounding Grenfall tower Getty In Pictures: Grenfell Tower after the fire Donated shoes sit in the Westway Sports Centre near to the site of the Grenfell Tower fire Getty Images In Pictures: Grenfell Tower after the fire Messages of support for those affected by the massive fire in Grenfell Tower are displayed on a well near the tower in London AP In Pictures: Grenfell Tower after the fire A local resident stands on her balcony by the gutted Grenfell Tower in Latimer Road Getty Images In Pictures: Grenfell Tower after the fire Messages of condolence are left at a relief centre close to the scene of the fire that broke out at Grenfell Tower, EPA In Pictures: Grenfell Tower after the fire A police officer stands by a security cordon outside Latimer Road station Getty Images In Pictures: Grenfell Tower after the fire Firemen examine the scorched facade of the Grenfell Tower in London on a huge ladder AP In Pictures: Grenfell Tower after the fire A search dog is led through the rubble of the Grenfell Tower in London as firefighting continue to damp-down the deadly fire AP In Pictures: Grenfell Tower after the fire Labour leader Jeremy Corbyn comforts a local resident (name not given) at St Clement's Church in west London where volunteers have provided shelter and support for people affected by the fire at Grenfell Tower David Mirzoeff/PA In Pictures: Grenfell Tower after the fire Labour leader Jeremy Corbyn hugs councillor Mushtaq Lasharie as he arrives at St Clement's Church in Latimer Road, where volunteers have provided shelter and support for people affected by the fire at Grenfell Tower Getty Images In Pictures: Grenfell Tower after the fire Labour leader Jeremy Corbyn meeting staff and volunteers at St Clementís Church in Latimer Road David Mirzoeff/PA In Pictures: Grenfell Tower after the fire Firefighters with a dog walk around the base of the Grenfell Tower REUTERS/Peter Nicholls In Pictures: Grenfell Tower after the fire Emotions run high as people attend a candle lit vigil outside Notting Hill Methodist Church near the 24 storey residential Grenfell Tower block in Latimer Road, West London Getty Images In Pictures: Grenfell Tower after the fire Debris hangs from the blackened exterior of Grenfell Tower Getty Images In Pictures: Grenfell Tower after the fire A woman speaks to Mayor of London Sadiq Khan outside Notting Hill Methodist Church near Grenfell Tower in west London after a fire engulfed the 24-storey building Yui Mok/PA Wire In Pictures: Grenfell Tower after the fire A woman holds a missing person posters near the Grenfell Tower block REUTERS/Stefan Wermuth In Pictures: Grenfell Tower after the fire Sadiq Khan speaking with a resident James Gourley/REX In Pictures: Grenfell Tower after the fire Ken Livingstone walks near the scene of the Grenfell Tower fire Getty Images In Pictures: Grenfell Tower after the fire Mayor of London Sadiq Khan is confronted by Kai Ramos, 7, near Grenfell Tower in west London after a fire engulfed the 24-storey building Yui Mok/PA Wire In Pictures: Grenfell Tower after the fire Mayor of London Sadiq Khan speaks to a woman outside Notting Hill Methodist Church near Grenfell Tower Yui Mok/PA Wire In Pictures: Grenfell Tower after the fire Volunteers distribute aid near Grenfell Tower Getty Images In Pictures: Grenfell Tower after the fire Family and friends of missing Jessica Urbano, 12, wearing photographs of Jessica pinned to their t-shirts gather near Grenfell Tower EPA In Pictures: Grenfell Tower after the fire Family and friends of missing Jessica Urbano, 12, wearing photographs of Jessica pinned to their t-shirts gather near Grenfell Tower EPA In Pictures: Grenfell Tower after the fire Family and friends of missing Jessica Urbano, 12, wearing photographs of Jessica pinned to their t-shirts gather near Grenfell Tower EPA In Pictures: Grenfell Tower after the fire People attend a vigil at Notting Hill Methodist Church near Grenfell Tower Getty Images In Pictures: Grenfell Tower after the fire People gather to observe a vigil outside St Clement's Church following the blaze at Grenfell Tower Getty Images In Pictures: Grenfell Tower after the fire People light candles as they observe a vigil outside St Clement's Church following the blaze at Grenfell Tower Getty Images In Pictures: Grenfell Tower after the fire People attend a vigil at Notting Hill Methodist Church near Grenfell Tower Getty Images In Pictures: Grenfell Tower after the fire A man distributes food from the back of a van near the scene of the fire which destroyed the Grenfell Tower block REUTERS/Paul Hackett In Pictures: Grenfell Tower after the fire A firefighter is cheered near the scene of the fire which destroyed the Grenfell Tower block REUTERS/Paul Hackett In Pictures: Grenfell Tower after the fire A T-shirt with a written message from the London Fire Brigade hangs from a fence near The Grenfell Tower block REUTERS/Stefan Wermuth In Pictures: Grenfell Tower after the fire A young girl on her way to lay flowers near Grenfell Tower Getty Images In Pictures: Grenfell Tower after the fire The remains of residential tower block Grenfell Tower are seen from Dixon House a nearby tower block Getty In Pictures: Grenfell Tower after the fire Volunteers prepare supplies for people affected by the Grenfell Tower block which was destroyed in a fire REUTERS/Neil Hall In Pictures: Grenfell Tower after the fire Volunteers move a car to make space for a lorry picking up supplies for people affected by the Grenfell Tower block REUTERS/Stefan Wermuth In Pictures: Grenfell Tower after the fire People distribute boxes of food near the scene of the fire which destroyed the Grenfell Tower bloc REUTERS/Paul Hackett In Pictures: Grenfell Tower after the fire A woman touches a missing poster for 12-year-old Jessica Urbano on a tribute wall after laying flowers on the side of Latymer Community Church next to the fire-gutted Grenfell Tower AP In Pictures: Grenfell Tower after the fire A man looks at messages written on a wall near the scene of the fire which destroyed the Grenfell Tower block REUTERS/Paul Hackett In Pictures: Grenfell Tower after the fire Candles and messages of condolence near where the fire broke out at Grenfell Tower EPA In Pictures: Grenfell Tower after the fire Police carry a stretcher towards Grenfell Tower Rick Findler/PA Wire In Pictures: Grenfell Tower after the fire Emergency services at Grenfell Tower Rick Findler/PA Wire In Pictures: Grenfell Tower after the fire Police carry out a body from Grenfell Tower in west London after a fire engulfed the 24-storey building Rick Findler/PA Wire

Mr Corbyn asked the Prime Minister to “immediately set out a clear, independent and thorough process for identifying and addressing the broader failings that led to the Grenfell fire”.

This should cover social housing policy and the relationship between residents and Kensington and Chelsea Borough Council, as well as its tenant management organisation, he said.

The Labour leader said he was “troubled” that the Government has only promised Grenfell survivors a 12-month immigration amnesty.

Amid concerns that some survivors are wary of speaking to authorities because of their immigration status, Mr Moore-Bick asked ministers to confirm that anyone living in the country illegally would not be deported. However, the Government has refused to extend the 12-month amnesty.