Ending the free movement of people from EU countries after Brexit may not result in lower overall migration, a committee of peers has warned.

No details on a new immigration system for EU nationals has been released, but the House of Lords EU Home Affairs Sub-Committee says net migration to the UK from outside the EU remains significantly higher than within it, despite non-EU migration already being covered by restrictions.

The wide-ranging assessment says: “Restoration of national control over EU migration may or may not, therefore, deliver a reduction in overall net migration.”

The committee concluded that cutting EU immigration is unlikely to provide a “quick fix” for low wages.

The report makes the case for a “two-way agreement” with the EU on migration, which would involve offering preferential treatment to EU nationals in return for reciprocal approach to UK nationals in the EU.

Before the referendum, leading figures in the Leave campaign argued for an Australian-style points-based immigration system, though nothing of that nature has been formally proposed or suggested by the Government. The peers’ report warns that any immigration system “hedged” with exemptions for particular economic sectors or schemes could produce the “worst of all worlds, failing to deliver a meaningful reduction in immigration while also proving more onerous and costly for employers, prospective applicants, and those charged with enforcement”.

Baroness Prashar, chair of the committee, said: “The precise manner in which the Government proposes to ‘end’ free movement is a pivotal aspect of the United Kingdom’s approach to negotiations with the European Union and could have far-reaching consequences for the UK’s future trading relationship with the EU.

“Crucial sectors of the economy depend on EU migrant labour, so it is essential that any changes don't endanger the vibrancy of the UK economy.

“We therefore recommend a phased transition to avoid short-term shocks to particular sectors.”

She added that the committee was “struck by the weaknesses and gaps in the UK’s migration statistics”.

A Home Office spokesman said: “Once we have left the European Union it will be the Government that sets our immigration rules.