MPs largely believe that allowing EU nationals already living and working in the UK to stay post-Brexit is compatible with delivering on the referendum result.
According to a new survey, just 5% of the 101 members interviewed said this was incompatible with leaving the EU.
But the research also found that 58% see controlling immigration from the EU as a key condition of respecting the June 23 vote.
It was carried out on behalf of UK in a Changing Europe and The Mile End Institute at Queen Mary University of London.
The survey also revealed few MPs believe the referendum result would not be honoured if Britain remained in the single market or continued to pay into the EU budget.
In a speech last month, Theresa May set out her plan to take the UK out of both the single market and customs union in its current form.
Other findings include reduced support for referenda in general and that MPs expected Remain to win.
Additionally, some 49% believe parliament should have a vote on the final deal agreed between the UK and EU, as the prime minister has promised.
But there is little appetite for a further referendum, as advocated by the Liberal Democrats.
Just 13% wanted a second referendum to approve or reject any deal with the EU.
Ipsos Mori’s Reputation Centre interviewed the sample of MPs between October 31 and December 21 last year.
The study was weighted to be a representative sample of the House, by party and frontbench-backbench status.
