Ministers must consider stripping immigration policy from the oversight of the Home Office post-Brexit, a new report has suggested after a string of high-profile failures at the department.

Citing "unrealistic" migration targets, the Windrush scandal and outrage over DNA tests, researchers at the Institute for Government (IfG) said the UK government's immigration policy "appears to be lurching from crisis to crisis".

Questioning the suitability of the department to deliver immigration reforms after the UK quits the EU, the IfG raised the possibility of the creation of a separate government department or public body.

It warned that unless there is radical reform at the Home Office, the government faces "an even bigger crisis than Windrush" in the coming years with an EU settlement scheme involving three-and-a-half million citizens eligible for settled status after Brexit.

"As things stand, the Home Office is not ready or able to meet the Brexit challenge on immigration," the report stated.

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"The government must now look at alternatives, including whether Whitehall needs a separate immigration department or whether a public body should be created to manage specific elements of the system - keeping the front line at arm's length from ministers."

It suggested the cabinet secretary – as part of a wider review of government machinery after Brexit – should assess whether the Home Office remains the right place for immigration policy.

Joe Owen, an associate director at the IfG, said: "As we end free movement from the EU, our migration policy must address the needs of the country but also the public confidence challenge.

"Ministers need to consider whether the Home Office is the right permanent home for a migration policy that needs to serve labour market needs, be fair and efficient in dealing with applicants, and provide the necessary degree of assurance to the wider public."

In a scathing assessment of the Conservatives' policy on immigration since 2010 – to "try and reduce it" – the report added that for over a decade the UK has lacked a "detailed" policy on immigration.

"A desire to reduce immigration, expressed through an aspirational target and a new approach to enforcement, does not count as a strategy," researchers claimed.

The report said policy to reduce net migration to the tens of thousands – one that has never been achieved by ministers – "has always been little more than a political tactic" and the government does not have the power to deliver it.

Responding to the report, the chief executive of Refugee Action charity, Stephen Hall, said: "Institutional failures at the Home Office are literally a matter of life and death for people seeking asylum in the UK. This report lays out the scale of the problems and a clear way forward.

"The home secretary must act now, setting clear short and longer-term objectives for the department and UK immigration policy."

A Home Office spokesperson said: “This report calls on the government to publish a clear vision for immigration, which the government has done through the white paper on the UK’s future skills-based immigration system, published last year.

“Our proposals would mean we have a single, skills-based immigration system that will allow us to attract the talented workers so that the UK prospers, but also delivers on the referendum result, ends free movement and improves border security.