Home Secretary Amber Rudd should resign over the Windrush scandal, Emily Thornberry has said.

The shadow foreign secretary, speaking on BBC One’s Andrew Marr Show, said there was something “rotten at the heart of Government” as she slammed the Home Office’s approach to immigration.

It comes after a slew of stories about members of the Windrush generation facing problems with access to healthcare and other state services.

Many in the Windrush generation – who arrived from the Caribbean between the late 1940s and 1970s – have no record of their status and have found it challenged under recent laws that require them to provide proof of near-continuous residence.

She said: “People have died, people have lost their jobs, lost their futures. People working in the national health service all their lives suddenly lose their jobs.

“It could not be worse and yet the Home Secretary thinks ‘I can apologise and it will be alright’. Well, it won’t be.

“I really think she should quit.”

When asked whether she believed ministers had implemented a racist policy, Ms Thornberry said: “I don’t like to bandy around these things, I’d rather just stick to the evidence.

“I’m happy to say there is something rotten at the heart of Government.

“I think that the idea of cutting immigration back to tens of thousands when you know you have no control over one of the major drivers and so, therefore, you need to be enforcing rules and be fundamentally unfair on those from outside the European Union, that is wrong and that is rotten.”

Justice Secretary David Gauke said the Home Secretary should not resign, telling the BBC: “No, absolutely, because when it comes down to it, the central policy is right.

“Clearly, there have been very significant failures in terms of how this has been implemented.

“I think it is right that both the Home Secretary and Prime Minister have apologised for this.”

Asked if he felt ashamed about what had happened, Mr Gauke said: “Yes. It is wrong what has happened. It should not have happened.”