The Home Affairs committee has said it is a "regrettable missed opportunity" that the Government has not attempted to build consensus on migration and engage in open debate and consultation on policy issues in the two years since the Referendum.
In its interim report of its Post Brexit migration policy enquiry the committee criticises the Government's failure, adding that continued delays to the White Paper on Immigration mean there is little indication of what any new migration policy will include.
Committee chair Yvette Cooper said: "The misinformation and tensions over immigration during the referendum campaign were deeply damaging and divisive. It is essential that does not happen again, and those who exploited concerns over immigration during the referendum need to be more honest and more responsible when it is debated in the run up to the final deal.
"We found there were a much wider range of possible precedents and options for immigration reform than people often talk about - including options that could be combined with participation in the single market - that we believe the Government should be exploring further now."
Sarah Cooper, chief executive of English UK, welcomed the committee's call for a public consultation.
She said: "We would really like to see more debate around this, particularly as previous surveys have shown that the public do not generally regard students as migrants. We are also unhappy that the Government has not shown any clarity on post-Brexit migration policy, as this is crucial to the future of our industry – and that of the wider international education sector."