Migration Watch said the UK's population will grow by 12.2m by 2039 unless the UK pushes for a so-called hard Brexit.
In a report published this morning, the organisation said remaining a full member of the Single Market will require continued acceptance of the free movement of people.
"This, combined with very large wage disparities between the UK and Eastern Europe and high levels of unemployment in Southern Europe, has led to very high levels of net migration from the EU," it said.
"There is no sign so far that the devaluation of sterling or [the Brexit vote] have had any significant effect on the net inflow.
"The increase due in the minimum wage will increase the attraction of the UK," it added.
However, the Liberal Democrats slammed the report. Leader Tim Farron accused Migration Watch of "pushing for a hard Brexit that would rip Britain out of the single market, costing jobs and risking the livelihoods of thousands of British people".
Organisations have warned a hard Brexit could widen the skills gap in the UK, with fewer high-skilled workers to fill specialist roles.
Although immigration hit a record high last year, the engineering industry has warned that a hard Brexit could delay some of the UK's largest engineering projects, including HS2 and the (already heavily delayed) Hinkley Point C power station.
In September, a study by LinkedIn showed the professional services, technology and finance sectors are all likely to be the hardest-hit by Brexit, as access to top talent is put at risk.