A new report from the House of Lords has found that net migration may not fall post-Brexit.
The EU home affairs sub-committee said that net migration – immigration minus emigration – was consistently higher from outside the EU. The Government is yet to outline a new immigration system for when Britain leaves the European Union.
A pledge has been made to reduce net migration to below 100,000 by 2020.
The report said: "The restoration of national control over EU migration may or may not deliver a reduction in overall net migration."
In the most recent official figures, covering the year to the end of September, both immigration and net migration from the EU were higher than that for the rest of the world for the first time.
Overall, net migration to the UK dropped to 273,000 in the year to September, down 49,000 from the previous year.
The committee report also said that a cut in EU migration was unlikely to provide a "quick fix" to low wages.
The committee endorsed the Government's intention to pursue a "two-way agreement" with the EU on future migration flows, and deemed it "vital" that the Government should not close off policy options on future regulation of EU immigration ahead of negotiations.
Elsewhere in the report it suggested that the UK should use a 'phased migration transition' in order to avoid a shock to businesses.
Chairman of the Committee, Baroness Prashar 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.